Re: [agi] Do the inference rules of categorical logic make sense?
Pei, Sorry for delayed reply. I answer point-by-point below. On 10/11/07, Pei Wang [EMAIL PROTECTED] wrote: Basic rule for evidence-based estimation of implication in NARS seems to be roughly along the lines of term construction in my framework (I think there's much freedom in its choice, do you have other variants of it/justification for current choice relative to other possibilities which is not concerned with applicability to derivation of rules for abduction/induction/etc.?), There is some justification behind the design of every inference rule (and its truth value function), not only abduction/induction. You can find most in the book, and many are also in my other publications. I meant the basic rule of evidence measuring that considers extension and intension sets. There certainly is a justification for it, but there obviously are alternatives, so my question is about the choice of this extension/intension measuring above other options. but I'm not sure about how you handle variations of structures (that is, how does system represents two structures which are similar in some sense and how it extracts the common part from them). It's difficult to see from basic rules if it's not addressed directly. The basic rules (deduction/abduction/induction/revision) ignore the internal structure of compound terms. There are special inference rules that handles the composition/decomposition of various compound structure. Again, they are mostly given by the book. I didn't mean the structure of compound terms, but the structure of experience representation, which consists of a set of individual statements and terms that describe that experience. For example, how will it see similarities and differences between 111222333 and ? Would it enable simple slippage between them? How will it learn these representations? Yes, the two can be recognized as similar, so the analogy rule can use one as the other in certain situations. It'd be interesting to get an idea of how such things can be translated to internal representation that implements these operations. Basic rule seems to require presence of terms at the same time, which for example can't be made neurologically plausible, unless semantics of terms is time-dependent (because neuron only knows that other neurons from which it received input fired some time in the past, and feature/term it represents if it chooses to fire is a statement about features represented by those other fired neurons in the past). It depends on what you mean by presence of terms at the same time. In NARS, all inference happens within a concept (because every inference rule requires two premises sharing a term), so as far as two beliefs are recalled at the same time, the basic rules can be applied. I mean the difference between experience of term in the present and experience of the same term (from I/O POV) that happened in the past. If these notions are represented by separate terms, how are they connected? I'm sorry if I'm asking about something that's being addressed in your book, I don't have a copy. Why do you need so many rules? I didn't expect so many rules myself at the beginning. I add new rules only when the existing ones are not enough for a situation. It will be great if someone can find a simpler design. I feel that some of complexity comes from modeling of natural language statements. Do you agree? -- Vladimir Nesovmailto:[EMAIL PROTECTED] - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=56112168-b226f2
Re: [agi] Do the inference rules of categorical logic make sense?
About NARS... Nesov/Wang dialogued: Why do you need so many rules? I didn't expect so many rules myself at the beginning. I add new rules only when the existing ones are not enough for a situation. It will be great if someone can find a simpler design. I feel that some of complexity comes from modeling of natural language statements. Do you agree? I think the complexity comes from the particular logical/algebraic formalism underlying NARS... In PLN, which is similar to NARS in some respects but with a probabilistic foundation, there are fewer rules because the underlying algebra is more powerful, allowing more cases in which rules may be derived from other rules. E.g. in NARS, induction and abduction are primary rules, whereas in PLN they are derived via combining Bayes rule with deduction in different (simple) ways. And in NARS, higher-order inference rules are posited separately than first-order inference rules, whereas in PLN most of the higher-order rules are derived directly from corresponding first-order rules. [Note that in PLN and NARS, the terms first-order and higher-order have different meanings than the ones often seen. First order term logic is the pure logic of inheritance with no explicit variables or quantifiers; higher-order term logic introduced quantified variables.] -- Ben G - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=56116649-ef41f9
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/21/07, Vladimir Nesov [EMAIL PROTECTED] wrote: Pei, Sorry for delayed reply. I answer point-by-point below. On 10/11/07, Pei Wang [EMAIL PROTECTED] wrote: Basic rule for evidence-based estimation of implication in NARS seems to be roughly along the lines of term construction in my framework (I think there's much freedom in its choice, do you have other variants of it/justification for current choice relative to other possibilities which is not concerned with applicability to derivation of rules for abduction/induction/etc.?), There is some justification behind the design of every inference rule (and its truth value function), not only abduction/induction. You can find most in the book, and many are also in my other publications. I meant the basic rule of evidence measuring that considers extension and intension sets. There certainly is a justification for it, but there obviously are alternatives, so my question is about the choice of this extension/intension measuring above other options. Sorry I still don't quite get your question. If you mean (1) why extension and intension are measured in a mixed manner, not separated, then I have a whole section (7.2) devoted to this issue in my book, and the summary is such a unified treatment is necessary for intelligence. If you mean (2) why the amount of evidence is defined as the size of the extension and intention of the related terms, then the answer directly follows from the definition of evidence, as given in many of my publications --- if what is defined as evidence only exists in those sets, then it is natural to use the size of the sets as the amount of evidence. but I'm not sure about how you handle variations of structures (that is, how does system represents two structures which are similar in some sense and how it extracts the common part from them). It's difficult to see from basic rules if it's not addressed directly. The basic rules (deduction/abduction/induction/revision) ignore the internal structure of compound terms. There are special inference rules that handles the composition/decomposition of various compound structure. Again, they are mostly given by the book. I didn't mean the structure of compound terms, but the structure of experience representation, which consists of a set of individual statements and terms that describe that experience. Experience is formally defined as the stream (not set) of incoming tasks, each of which can be (1) new knowledge (a statement with a truth value), (2) question (a statement without a truth value), or (3) goal (a statement with a desire value). For example, how will it see similarities and differences between 111222333 and ? Would it enable simple slippage between them? How will it learn these representations? Yes, the two can be recognized as similar, so the analogy rule can use one as the other in certain situations. It'd be interesting to get an idea of how such things can be translated to internal representation that implements these operations. It's a long story, and there are many possibilities, but basically, it is about the positive and negative evidence of the following similarity statement: (* (* 1 1 1) (* 2 2 2) (* 3 3 3)) - (* (* 1 1 1 1) (* 2 2 2 2) (* 3 3 3 3)) Basic rule seems to require presence of terms at the same time, which for example can't be made neurologically plausible, unless semantics of terms is time-dependent (because neuron only knows that other neurons from which it received input fired some time in the past, and feature/term it represents if it chooses to fire is a statement about features represented by those other fired neurons in the past). It depends on what you mean by presence of terms at the same time. In NARS, all inference happens within a concept (because every inference rule requires two premises sharing a term), so as far as two beliefs are recalled at the same time, the basic rules can be applied. I mean the difference between experience of term in the present and experience of the same term (from I/O POV) that happened in the past. If these notions are represented by separate terms, how are they connected? Well, if past experience and current experience involve the same concept, they will use the same term. You may want to see the actual examples in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt and http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt I'm sorry if I'm asking about something that's being addressed in your book, I don't have a copy. I'm sorry to say that if you are seriously interested in NARS, you do need to read the book. If your library doesn't have it, it may be obtained through inter-library loan. If you have absolutely no way to get it, send me a private email and I'll arrange something. Why do you need so many rules? I didn't expect so many rules myself
Re: [agi] Do the inference rules of categorical logic make sense?
The difference between NARS and PLN has much more to do with their different semantics, than with their different logical/algebraic formalism. For example, according to the semantics of NARS, Bayes rule, with all of its variants, is deduction. Therefore it is impossible to use on induction/abduction/... Also, in NARS the higher-order inference rules are mostly isomorphic to first-order inference rules, in the sense that they use the same truth value function, and there is one-to-one mappings between them --- see http://nars.wang.googlepages.com/wang.abduction.pdf for people who don't have the book. Pei On 10/21/07, Benjamin Goertzel [EMAIL PROTECTED] wrote: About NARS... Nesov/Wang dialogued: Why do you need so many rules? I didn't expect so many rules myself at the beginning. I add new rules only when the existing ones are not enough for a situation. It will be great if someone can find a simpler design. I feel that some of complexity comes from modeling of natural language statements. Do you agree? I think the complexity comes from the particular logical/algebraic formalism underlying NARS... In PLN, which is similar to NARS in some respects but with a probabilistic foundation, there are fewer rules because the underlying algebra is more powerful, allowing more cases in which rules may be derived from other rules. E.g. in NARS, induction and abduction are primary rules, whereas in PLN they are derived via combining Bayes rule with deduction in different (simple) ways. And in NARS, higher-order inference rules are posited separately than first-order inference rules, whereas in PLN most of the higher-order rules are derived directly from corresponding first-order rules. [Note that in PLN and NARS, the terms first-order and higher-order have different meanings than the ones often seen. First order term logic is the pure logic of inheritance with no explicit variables or quantifiers; higher-order term logic introduced quantified variables.] -- Ben G This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=56145391-2cb7f6
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/21/07, Pei Wang [EMAIL PROTECTED] wrote: The difference between NARS and PLN has much more to do with their different semantics, than with their different logical/algebraic formalism. Sure; in both cases, the algebraic structure of the rules and the truth-value formulas follow from the semantics For example, according to the semantics of NARS, Bayes rule, with all of its variants, is deduction. Therefore it is impossible to use on induction/abduction/... For the benefit of others besides Pei ... what I meant was that inferences like A -- B A -- C |- B -- C and A -- C B -- C |- A -- B are handled in PLN via a combination of Bayes rule and deduction, whereas in NARS they are handled by special induction and abduction truth value formulas... -- Ben - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=56156686-9d128e
Re: [agi] Do the inference rules of categorical logic make sense?
Mike Tintner wrote: Charles H:as I understand it, this still wouldn't be an AGI, but merely a categorizer. That's my understanding too. There does seem to be a general problem in the field of AGI, distinguishing AGI from narrow AI - philosophically. In fact, I don't think I've seen any definition of AGI or intelligence that does. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; But *do* notice that the terminal nodes are uninterpreted. This means that they could be assigned, e.g., procedural values. Because of this, even though the current design (as I understand it) of NARS is purely a categorizer, it's not limited in what it's extensions and embedding environment can be. It would be a trivial extension to allow terminal nodes to have a type, and that what was done when a terminal node was generated could depend upon that type. (There's a paper called wang.roadmap.pdf that I *must* get around to reading!) P.S.: In the paper on computations it seems to me that items of high durability should not be dropped from the processing queue even if it becomes full of higher priority tasks. There should probably be a postponed tasks location where things like garbage collection and database sanity checking and repair can be saved to be done during future idle times. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52084316-6120bf
Re: [agi] Do the inference rules of categorical logic make sense?
Linas Vepstas wrote: On Sun, Oct 07, 2007 at 12:36:10PM -0700, Charles D Hixson wrote: Edward W. Porter wrote: Fred is a human Fred is an animal You REALLY can't do good reasoning using formal logic in natural language...at least in English. That's why the invention of symbolic logic was so important. I suppose this was pounded to death in the rest of the thread, (which I haven't read) but still: syllogistic reasoning does occur in hypothesis formation, and thus, learning: -- maybe humans are animals? What evidence do I have to support this? -- maybe animals are human? Can that be? If Fred has an artificial heart, then perhaps he isn't simply just a special case of an animal. If some pig has human organs in it, then perhaps its an animal that is human. Neither syllogistic deduction is purely false in the real world; there is an it depends aspect to it. learning AI would chalk it up as a maybe, and see is this reasoning leads anywhere. I beleive Pei Wang's NARS system tries to do this; it seems more structured than the fuzzy logic type approaches that antedate it. --linas For me the sticking point was that we were informed that we didn't know anything about anything outside of the framework presented. We didn't know what a Fred was, or what a human was, or what an animal was. A Fred could be a audio frequency of 440 Hz for all we knew. And telling us that he was a human didn't rule that out, because we didn't know what a human was either. Your extension questions make sense if we aren't dealing with a tabula rasa. But we were explicitly told that we were, so the answers to your questions would have been ??? and none and ??? and no evidence. Your hypothetical extensions are also only considerable in the context of extensive knowledge that was specified as unknown. OTOH, the context was really about NARS. (I feel that my objections still apply, but not as strongly. If I had understood what was being discussed as well then as I do now, I would have commented less strongly.) - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52086180-e7e4ee
Re: [agi] Do the inference rules of categorical logic make sense?
Mark Waser wrote: Thus, as I understand it, one can view all inheritance statements as indicating the evidence that one instance or category belongs to, and thus is “a child of” another category, which includes, and thus can be viewed as “a parent” of the other. Yes, that is inheritance as Pei uses it. But are you comfortable with the fact that I am allowed to drink alcohol is normally both the parent and the child of I am an adult (and vice versa)? How about the fact that most ravens are black is both the parent and child of this raven is white (and vice versa)? Since inheritance relations are transitive, the resulting hierarchy of categories involves nodes that can be considered ancestors (i.e., parents, parents of parents, etc.) of others and nodes that can be viewed as descendents (children, children of children, etc.) of others. And how often do you really want to do this with concepts like the above -- or when the evidence is substantially less than unity? And loops and transitivity are really ugly . . . . NARS really isn't your father's inheritance. A definite point, and one that argues against my model of a prototype based computer language. I prefer to think in lattice structures rather than in directed graphs. Another problem is the matter of probability and stability values being attached to the links. I definitely need a better model. To continue your point, just because A--B at one point in time doesn't ensure that it will also be true (with a probability above any particular threshold)at a later point. Links, especially low stability links, get re-evaluated, where prototype descendants maintain their ancestry. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52089907-ea36e2
Re: [agi] Do the inference rules of categorical logic make sense?
Pei, (Sorry for a long list of questions; maybe I'm trying to see NARS as what it isn't, through lens of my own approach.) Do you have a high-level description of how statements evolve during learning of complex descriptions, including creation of new subsymbolic terms (compound terms)? Basic rule for evidence-based estimation of implication in NARS seems to be roughly along the lines of term construction in my framework (I think there's much freedom in its choice, do you have other variants of it/justification for current choice relative to other possibilities which is not concerned with applicability to derivation of rules for abduction/induction/etc.?), but I'm not sure about how you handle variations of structures (that is, how does system represents two structures which are similar in some sense and how it extracts the common part from them). It's difficult to see from basic rules if it's not addressed directly. For example, how will it see similarities and differences between 111222333 and ? Would it enable simple slippage between them? How will it learn these representations? Do you address temporal activation of terms, where term being active is a temporal statement expressed as relative to current moment, and learning of structure results from prolonged cooccurrence of its components? Basic rule seems to require presence of terms at the same time, which for example can't be made neurologically plausible, unless semantics of terms is time-dependent (because neuron only knows that other neurons from which it received input fired some time in the past, and feature/term it represents if it chooses to fire is a statement about features represented by those other fired neurons in the past). Why do you need so many rules? Ultimately all you need are rules for term formation (for which intersection as starting point seems to be enough) and term activation given currently active terms (fluid inference). Is there a basic set which is theoretically sufficient, although probably requires too much indirect support structures (I assume that input/output experience is presented as flat conjunction of active terms)? Why do you need to separately regard operations on terms and statements (and why statements have any significance in themselves, other than specific interpretation of underlying term activation rule)? On 10/10/07, Pei Wang [EMAIL PROTECTED] wrote: In NARS, the Deduction/Induction/Abduction trio has (at least) three different-though-isomorphic forms, one on inheritance, one on implication, and one mixed. For people who don't have access to the book, see http://nars.wang.googlepages.com/wang.abduction.pdf , though the symbols used in that paper is slightly different from the current form. Pei -- Vladimir Nesovmailto:[EMAIL PROTECTED] - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52127503-7a35a9
Re: [agi] Do the inference rules of categorical logic make sense?
Charles, I don't see - no doubt being too stupid - how what you are saying is going to make a categorizer into more than that - into a system that can, say, go on to learn various logic's, or how to build a house or other structures or tell a story - that can be a *general* intelligence. What struck me about the overall discussion of NARS' logical capabilities, firstly, was that they all depended - I think you may have made this point - on everyone's *common sense* interpretations of inheritance and other relations and the logic generally. In other words, any logic is - and always will be - a very *secondary* sign system for both representing and reasoning about the world. It is a highly evolved derivative of more basic, common sense systems in the brain - and, like language itself, has continually to be made sense of by the brain. (That's why I would suspect that all of you, however versed in logic you are, will, while looking at those logical propositions, go fuzzy from time to time - when your brain can't for a while literally make sense of them). A hierarchy of abstract/ concrete sign systems, grounded in the senses, is - I believe - essential for any AGI and general learning - and, NARS, AFAICT, lacks that. Secondly, I don't see how what you are saying will give NARS the ability to *create* new rules and strategies for its activities, (that are not derived from existing rules). AFAICT it simply applies logic and follows rules, even though they include rules for modifying rules. It cannot, like Pei or Bayes have done, create or fundamentally extend logics. If so, it is still narrow AI, not AGI. (There is, I repeat, a major need for a philosophical distinction between AI and AGI - in talking about the area of the last paragraph, I think we all flounder and grope for terms). Mike Tintner wrote: Charles H:as I understand it, this still wouldn't be an AGI, but merely a categorizer. That's my understanding too. There does seem to be a general problem in the field of AGI, distinguishing AGI from narrow AI - philosophically. In fact, I don't think I've seen any definition of AGI or intelligence that does. But *do* notice that the terminal nodes are uninterpreted. This means that they could be assigned, e.g., procedural values. Because of this, even though the current design (as I understand it) of NARS is purely a categorizer, it's not limited in what it's extensions and embedding environment can be. It would be a trivial extension to allow terminal nodes to have a type, and that what was done when a terminal node was generated could depend upon that type. (There's a paper called wang.roadmap.pdf that I *must* get around to reading!) P.S.: In the paper on computations it seems to me that items of high durability should not be dropped from the processing queue even if it becomes full of higher priority tasks. There should probably be a postponed tasks location where things like garbage collection and database sanity checking and repair can be saved to be done during future idle times. Version: 7.5.488 / Virus Database: 269.14.6/1060 - Release Date: 09/10/2007 16:43 - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52128101-e8e3f7
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/10/07, Vladimir Nesov [EMAIL PROTECTED] wrote: Pei, (Sorry for a long list of questions; maybe I'm trying to see NARS as what it isn't, through lens of my own approach.) Do you have a high-level description of how statements evolve during learning of complex descriptions, including creation of new subsymbolic terms (compound terms)? Nothing too detail, but you can start from the paper I co-authored with Hofstadter, especially on the discussion on Compositionality and Categorical dynamics. I don't call the compound terms subsymbolic. Basic rule for evidence-based estimation of implication in NARS seems to be roughly along the lines of term construction in my framework (I think there's much freedom in its choice, do you have other variants of it/justification for current choice relative to other possibilities which is not concerned with applicability to derivation of rules for abduction/induction/etc.?), There is some justification behind the design of every inference rule (and its truth value function), not only abduction/induction. You can find most in the book, and many are also in my other publications. but I'm not sure about how you handle variations of structures (that is, how does system represents two structures which are similar in some sense and how it extracts the common part from them). It's difficult to see from basic rules if it's not addressed directly. The basic rules (deduction/abduction/induction/revision) ignore the internal structure of compound terms. There are special inference rules that handles the composition/decomposition of various compound structure. Again, they are mostly given by the book. For example, how will it see similarities and differences between 111222333 and ? Would it enable simple slippage between them? How will it learn these representations? Yes, the two can be recognized as similar, so the analogy rule can use one as the other in certain situations. Do you address temporal activation of terms, where term being active is a temporal statement expressed as relative to current moment, and learning of structure results from prolonged cooccurrence of its components? Yes, to a degree, though not in the same way as neural network. I'm sorry that I don't have the time to give a detailed explanation on this topic. Basic rule seems to require presence of terms at the same time, which for example can't be made neurologically plausible, unless semantics of terms is time-dependent (because neuron only knows that other neurons from which it received input fired some time in the past, and feature/term it represents if it chooses to fire is a statement about features represented by those other fired neurons in the past). It depends on what you mean by presence of terms at the same time. In NARS, all inference happens within a concept (because every inference rule requires two premises sharing a term), so as far as two beliefs are recalled at the same time, the basic rules can be applied. Whether NARS rules are neurologically plausible is not a major consideration for me. NARS is not a brain model. Why do you need so many rules? I didn't expect so many rules myself at the beginning. I add new rules only when the existing ones are not enough for a situation. It will be great if someone can find a simpler design. Ultimately all you need are rules for term formation (for which intersection as starting point seems to be enough) and term activation given currently active terms (fluid inference). Is there a basic set which is theoretically sufficient, although probably requires too much indirect support structures (I assume that input/output experience is presented as flat conjunction of active terms)? Maybe, but until I see a concrete design, I cannot be sure. Why do you need to separately regard operations on terms and statements (and why statements have any significance in themselves, other than specific interpretation of underlying term activation rule)? Not fully separate. Statements in many cases are treated just like other terms. However, since statements are terms with truth value, they do need special treatment here or there, which don't make sense for other (non-statement) terms. Pei On 10/10/07, Pei Wang [EMAIL PROTECTED] wrote: In NARS, the Deduction/Induction/Abduction trio has (at least) three different-though-isomorphic forms, one on inheritance, one on implication, and one mixed. For people who don't have access to the book, see http://nars.wang.googlepages.com/wang.abduction.pdf , though the symbols used in that paper is slightly different from the current form. Pei -- Vladimir Nesovmailto:[EMAIL PROTECTED] - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To
Re: [agi] Do the inference rules of categorical logic make sense?
On Wed, Oct 10, 2007 at 01:06:35PM -0700, Charles D Hixson wrote: For me the sticking point was that we were informed that we didn't know anything about anything outside of the framework presented. We didn't know what a Fred was, or what a human was, or what an animal was. ?? Well, no. In NARS, you actually know a lot more; you know the relative position of each statement in the lattice of posets, and that is actually a very powerful bit of knowledge. From this, you can compute a truth value, and evidence, for the statements. NARS tells you how to combine the truth values. So, while you might not explicitly know what Fred is, you do have to compute a truth value for fred is an animal and fred is a human. NARS then tells you what the corresponding evidence is for an animal is a human and a human is an animal (presumably the evidence is weak, and strong, depending on the relation of these posets within the universe.) In measure-theoreic terms, the truth value is the measure of the size of the poset relative the size of the universe. NARS denotes this by the absolute value symbol. The syllogism rules suggest how the measures of the various intersections and unions of the posets need to be combined. I presume that maybe there is some theorem that shows that the NARS system assigns evidence values that are consistent with the axioms of measure theory. Seems reasonable to me; I haven't thought it through, and I haven't read more in that direction. --linas - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52168417-2fb31b
Re: [agi] Do the inference rules of categorical logic make sense?
Mike Tintner wrote: Charles, I don't see - no doubt being too stupid - how what you are saying is going to make a categorizer into more than that - into a system that can, say, go on to learn various logic's, or how to build a house or other structures or tell a story - that can be a *general* intelligence. I wouldn't say you were being stupid. Nobody knows how to build an AGI yet. And I'm envisioning the current system of NARS as only a component, albeit an important component. (I don't know how Pei Wang is envisioning it.) But if you study the input system from the eye (overview...I have no detailed knowledge), you discover that the initial sensory stimuli are split into several streams that are processed separately (possibly categorized) and then recombined. Sometimes something very important will jump out of the system, however, and cause rapid reactions that the consciousness never becomes aware of noticing before acting on. (N.B.: This being aware of before acting on is often-to-usually an hallucination.) Clearly some categorizer has noticed that something was VERY important. As such, apparently some kind of categorizer is very important. My suspicion is that most categorizers work with small databases in restricted domains, acting as black-box functions...though function isn't the right word for something that can return multiple results. What struck me about the overall discussion of NARS' logical capabilities, firstly, was that they all depended - I think you may have made this point - on everyone's *common sense* interpretations of inheritance and other relations and the logic generally. In other words, any logic is - and always will be - a very *secondary* sign system for both representing and reasoning about the world. It is a highly evolved derivative of more basic, common sense systems in the brain - and, like language itself, has continually to be made sense of by the brain. (That's why I would suspect that all of you, however versed in logic you are, will, while looking at those logical propositions, go fuzzy from time to time - when your brain can't for a while literally make sense of them). A hierarchy of abstract/ concrete sign systems, grounded in the senses, is - I believe - essential for any AGI and general learning - and, NARS, AFAICT, lacks that. Secondly, I don't see how what you are saying will give NARS the ability to *create* new rules and strategies for its activities, (that are not derived from existing rules). AFAICT it simply applies logic and follows rules, even though they include rules for modifying rules. It cannot, like Pei or Bayes have done, create or fundamentally extend logics. If so, it is still narrow AI, not AGI. (There is, I repeat, a major need for a philosophical distinction between AI and AGI - in talking about the area of the last paragraph, I think we all flounder and grope for terms). Mike Tintner wrote: Charles H:as I understand it, this still wouldn't be an AGI, but merely a categorizer. That's my understanding too. There does seem to be a general problem in the field of AGI, distinguishing AGI from narrow AI - philosophically. In fact, I don't think I've seen any definition of AGI or intelligence that does. But *do* notice that the terminal nodes are uninterpreted. This means that they could be assigned, e.g., procedural values. Because of this, even though the current design (as I understand it) of NARS is purely a categorizer, it's not limited in what it's extensions and embedding environment can be. It would be a trivial extension to allow terminal nodes to have a type, and that what was done when a terminal node was generated could depend upon that type. (There's a paper called wang.roadmap.pdf that I *must* get around to reading!) P.S.: In the paper on computations it seems to me that items of high durability should not be dropped from the processing queue even if it becomes full of higher priority tasks. There should probably be a postponed tasks location where things like garbage collection and database sanity checking and repair can be saved to be done during future idle times. Version: 7.5.488 / Virus Database: 269.14.6/1060 - Release Date: 09/10/2007 16:43 - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52174802-a2d0ec
Re: [agi] Do the inference rules of categorical logic make sense?
Generally, yes, you know more. In this particular instance we were told the example was all that was known. Linas Vepstas wrote: On Wed, Oct 10, 2007 at 01:06:35PM -0700, Charles D Hixson wrote: For me the sticking point was that we were informed that we didn't know anything about anything outside of the framework presented. We didn't know what a Fred was, or what a human was, or what an animal was. ?? Well, no. In NARS, you actually know a lot more; you know the relative position of each statement in the lattice of posets, and that is actually a very powerful bit of knowledge. From this, you can compute a truth value, and evidence, for the statements. NARS tells you how to combine the truth values. So, while you might not explicitly know what Fred is, you do have to compute a truth value for fred is an animal and fred is a human. NARS then tells you what the corresponding evidence is for an animal is a human and a human is an animal (presumably the evidence is weak, and strong, depending on the relation of these posets within the universe.) In measure-theoreic terms, the truth value is the measure of the size of the poset relative the size of the universe. NARS denotes this by the absolute value symbol. The syllogism rules suggest how the measures of the various intersections and unions of the posets need to be combined. I presume that maybe there is some theorem that shows that the NARS system assigns evidence values that are consistent with the axioms of measure theory. Seems reasonable to me; I haven't thought it through, and I haven't read more in that direction. --linas - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=52175736-6ccdee
Re: [agi] Do the inference rules of categorical logic make sense?
It looks to me as if NARS can be modeled by a prototype based language with operators for is an ancestor of and is a descendant of. I don't believe that this is the case at all. NARS correctly handles cases where entities co-occur or where one entity implies another only due to other entities/factors. Is an ancestor of and is a descendant of has nothing to do with this. To me a model can well be dynamic and experience based. In fact I wouldn't consider a model very intelligent if it didn't either itself adapt itself to experience, or it weren't embedded in a matrix which adapted it to experiences. (This doesn't seem to be quite the same meaning that you use for model. Your separation of the rules of inference, the rational faculty, and the model as a fixed and unchanging condition don't match my use of the term. And your use of the term is better than his use of the term because . . . . ?:-) By model, he means model of cognition. For him (and all of us), cognition is dynamic and experience-based but the underlying process is relatively static and the same from individual to individual. I still find that I am forced to interpret the inheritance relationship as a is a child of relationship. Which is why you're having problems understanding NARS. If you can't get past this, you're not going to get it. And I find the idea of continually calculating the powerset of inheritance relationships unappealing. There may not be a better way, but if there isn't, than AGI can't move forwards without vastly more powerful machines. This I agree with. My personal (hopefully somewhat informed) opinion is that NARS (and Novamente) are doing more than absolutely needs to be done for AGI. Time will tell. I do feel that the limited sensory modality of the environment (i.e., reading the keyboard) makes AGI unlikely to be feasible. It seems to me that one of the necessary components of true intelligence is integrating multi-modal sensory experience. Why? - Original Message - From: Charles D Hixson [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Monday, October 08, 2007 5:50 PM Subject: Re: [agi] Do the inference rules of categorical logic make sense? OK. I've read the paper, and don't see where I've made any errors. It looks to me as if NARS can be modeled by a prototype based language with operators for is an ancestor of and is a descendant of. I do have trouble with the language terms that you use, though admittedly they appear to be standard for logicians (to the extent that I'm familiar with their dialect). That might well not be a good implementation, but it appears to be a reasonable model. To me a model can well be dynamic and experience based. In fact I wouldn't consider a model very intelligent if it didn't either itself adapt itself to experience, or it weren't embedded in a matrix which adapted it to experiences. (This doesn't seem to be quite the same meaning that you use for model. Your separation of the rules of inference, the rational faculty, and the model as a fixed and unchanging condition don't match my use of the term. I might pull out the rules of inference as separate pieces and stick them into a datafile, but datafiles can be changed, if anything, more readily than programs...and programs are readily changeable. To me it appears clear that much of the language would need to be interpretive rather than compiled. One should pre-compile what one can for the sake of efficiency, but with the knowledge that this sacrifices flexibility for speed. I still find that I am forced to interpret the inheritance relationship as a is a child of relationship. And I find the idea of continually calculating the powerset of inheritance relationships unappealing. There may not be a better way, but if there isn't, than AGI can't move forwards without vastly more powerful machines. Probably, however, the calculations could be shortcut by increasing the local storage a bit. If each node maintained a list of parents and children, and a count of descendants and ancestors it might suffice. This would increase storage requirements, but drastically cut calculation and still enable the calculation of confidence. Updating the counts could be saved for dreamtime. This would imply that during the early part of learning sleep would be a frequent necessity...but it should become less necessary as the ratio of extant knowledge to new knowledge learned increased. (Note that in this case the amount of new knowledge would be a measured quantity, not an arbitrary constant.) I do feel that the limited sensory modality of the environment (i.e., reading the keyboard) makes AGI unlikely to be feasible. It seems to me that one of the necessary components of true intelligence is integrating multi-modal sensory experience. This doesn't necessarily mean vision and touch, but SOMETHING. As such I can see NARS (or some
Re: [agi] Do the inference rules of categorical logic make sense?
When looking at it through a crisp glass, the relation is a preorder, not a (partial) order. And priming is essential. For example, in certain contexts, we think that an animal is a human (anthropomorphism). On 10/9/07, Mark Waser [EMAIL PROTECTED] wrote: Ack! Let me rephrase. Despite the fact that Pei always uses the words of inheritance (and is technically correct), what he means is quite different from what most people assume that he means. You are stuck on the common meanings of the terms is an ancestor of and is a descendant of and it's impeding your understanding. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51437008-630e6a
RE: [agi] Do the inference rules of categorical logic make sense?
properties or elements). Although I understand there is an importance equivalence between down in the comp hierarchical and up in the gen hierarchy, and that the two could be viewed as one hierarchy, I have preferred to think of them as different hierarchies, because the type of gens one gets by going up in the gen hierarchy tend to be different than the type of gens one gets by going down in the comp hierarchy. Each possible set in the powerset (the set of all subsets) of elements (eles), relationships (rels), attributes (atts) and contextual patterns (contextual pats) could be considered as possible generalizations. I have assumed, as does Goertzels Novamente, that there is a competitive ecosystem for representational resources, in which only the fittest pats and gens -- as determined by some measure of usefulness to the system -- survive. There are several major uses of gens, such as aiding in perception, providing inheritance of significant implication, providing appropriate level of representation for learning, and providing invariant representation in higher level comps. Although temporary gens will be generated at a relatively high frequency, somewhat like the inductive implications in NARS, the number of gens that survive and get incorporated into a lot of comps and episodic reps, will be an infinitesimal fraction of the powerset of eles, rels, atts, and contextual features stored in the system. Pats in the up direction in the Gen hierarchy will tend to be ones that have been selected for the usefulness as generalizations. They will often have reasonable number of features that correspond to that of their species node, but with some of them more broadly defined. The gens found by going down in the comp hierarchy are ones that have been selected for their representational value in a comp, and many of them would not normally be that valuable as what we normally think of as generalizations. In the type of system I have been thinking of I have assumed there will be substantially less multiple inheritance in the up direction in the gen hierarchy than in the down direction in the comp hierarchy (in which there would be potential inheritance from every ele, rel, att, and contextual feature of in a comps descendant nodes at multiple levels in the comp hierarchy below it. Thus, for spreading activation control purposes, I think it is valuable to distinguish between generalization and compositional hierarchies, although I understand they have an important equivalence that should not be ignored. I wonder if NARS makes such a distinction. These are only initial thoughts. I hope to become part of a team that gets an early world-knowledge computing AGI up and running. Perhaps when I do feedback from reality will change my mind. I would welcome comments, not only from Mark, but also from other readers. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 9:46 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? I don't believe that this is the case at all. NARS correctly handles cases where entities co-occur or where one entity implies another only due to other entities/factors. Is an ancestor of and is a descendant of has nothing to do with this. Ack! Let me rephrase. Despite the fact that Pei always uses the words of inheritance (and is technically correct), what he means is quite different from what most people assume that he means. You are stuck on the common meanings of the terms is an ancestor of and is a descendant of and it's impeding your understanding. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51480730-4665d4
Re: [agi] Do the inference rules of categorical logic make sense?
RE: [agi] Do the inference rules of categorical logic make sense?Thus, as I understand it, one can view all inheritance statements as indicating the evidence that one instance or category belongs to, and thus is a child of another category, which includes, and thus can be viewed as a parent of the other. Yes, that is inheritance as Pei uses it. But are you comfortable with the fact that I am allowed to drink alcohol is normally both the parent and the child of I am an adult (and vice versa)? How about the fact that most ravens are black is both the parent and child of this raven is white (and vice versa)? Since inheritance relations are transitive, the resulting hierarchy of categories involves nodes that can be considered ancestors (i.e., parents, parents of parents, etc.) of others and nodes that can be viewed as descendents (children, children of children, etc.) of others. And how often do you really want to do this with concepts like the above -- or when the evidence is substantially less than unity? And loops and transitivity are really ugly . . . . NARS really isn't your father's inheritance. - Original Message - From: Edward W. Porter To: agi@v2.listbox.com Sent: Tuesday, October 09, 2007 12:24 PM Subject: RE: [agi] Do the inference rules of categorical logic make sense? RE: (1) THE VALUE OF CHILD OF AND PARENT OF RELATIONS(2) DISCUSSION OF POSSIBLE VALUE IN DISTINGUISHING BETWEEN GENERALIZATIONAL AND COMPOSITIONAL INHERITANCE HIERARCHIES. Re Mark Waser's 10/9/2007 9:46 AM post: Perhaps Mark understands something I don't. I think relations that can be viewed as child of and parent of in a hierarchy of categories are extremely important (for reasons set forth in more detail below) and it is not clear to me that Pei meant something other than this. If Mark or anyone else has reason to believe that what [Pei] means is quite different than such child of and parent of relations, I would appreciate being illuminated by what that different meaning is. My understanding of NARS is that it is concerned with inheritance relations, which as I understand it, indicate the truth value of the assumption that one category falls within another category, where category is broadly defined to included not only what we normally think of as categories, but also relationships, slots in relationships, and categories defined by a sets of one or more properties, attributes, elements, relationships, or slot in relationships. Thus, as I understand it, one can view all inheritance statements as indicating the evidence that one instance or category belongs to, and thus is a child of another category, which includes, and thus can be viewed as a parent of the other. Since inheritance relations are transitive, the resulting hierarchy of categories involves nodes that can be considered ancestors (i.e., parents, parents of parents, etc.) of others and nodes that can be viewed as descendents (children, children of children, etc.) of others. I tend to think of similarity as a sibling relationship under a shared hidden parent category -- based on similar aspects of the sibling's extensions and/or intensions. In much of my own thinking I have thought of such categorization relations as is generalization, in which the parent is the genus, and the child is the species. Generalization is important for many reasons. First, perception is trying to figure which in category or generalization of things, actions, or situations various parts of a current set of sensory information might fit. Secondly, Generalization is important because it is necessary for implication. All those Bayesian probabilities we are used to thinking about such as P(A|B,C), are totally useless unless we have some way of knowing the probability the situation being considered contains a B or C. To do that you have to have categories that help you determine the extent to which a B or a C is present. To understand the implication of P(A|B,C) you have to have some meaning for the category A. Generalization is important for behavior because one uses generalization learned from past experiences to develop plans for how to achieve goals, and because most action schema are usually generalization that have to be instantiated in a context specific way. One of the key problems in AI has been non-literal matching. That is why representation schemes that have a flexibility something like that of NARS are necessary for any intelligence capable of operating well in anything other than limited domains. That is why so-called invariant or hierarchical memory representations are so valuable. This is indicated in writings of Jeff Hawkins, Thomas Serre (Learning a Dictionary of Shape-Components in Visual Cortex: Comparison with Neurons, Humans and Machines, by Thomas Serre, the google-able article I have cited so many times), and many others
RE: [agi] Do the inference rules of categorical logic make sense?
Mark, Thank you for your reply. I just ate a lunch with too much fat (luckily largely olive oil) in it so, my brain is a little sleepy. If it is not too much trouble could you please map out the inheritance relationships from which one derives how I am allowed to drink alcohol is both a parent and the child of I am an adult. And could you please do the same with how most ravens are balck is both parent and child of this raven is white. Most of the discussion I read in Pei's article related to inheritance relations between terms, that operated as subject and predicates in sentences that are inheritance statements, rather than between entire statemens, unless the statement was a subject or a predicate of a higher order inheritance statement. So what you are referring to appears to be beyond what I have read. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 12:47 PM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Thus, as I understand it, one can view all inheritance statements as indicating the evidence that one instance or category belongs to, and thus is a child of another category, which includes, and thus can be viewed as a parent of the other. Yes, that is inheritance as Pei uses it. But are you comfortable with the fact that I am allowed to drink alcohol is normally both the parent and the child of I am an adult (and vice versa)? How about the fact that most ravens are black is both the parent and child of this raven is white (and vice versa)? Since inheritance relations are transitive, the resulting hierarchy of categories involves nodes that can be considered ancestors (i.e., parents, parents of parents, etc.) of others and nodes that can be viewed as descendents (children, children of children, etc.) of others. And how often do you really want to do this with concepts like the above -- or when the evidence is substantially less than unity? And loops and transitivity are really ugly . . . . NARS really isn't your father's inheritance. - Original Message - From: Edward W. mailto:[EMAIL PROTECTED] Porter To: agi@v2.listbox.com Sent: Tuesday, October 09, 2007 12:24 PM Subject: RE: [agi] Do the inference rules of categorical logic make sense? RE: (1) THE VALUE OF CHILD OF AND PARENT OF RELATIONS(2) DISCUSSION OF POSSIBLE VALUE IN DISTINGUISHING BETWEEN GENERALIZATIONAL AND COMPOSITIONAL INHERITANCE HIERARCHIES. Re Mark Wasers 10/9/2007 9:46 AM post: Perhaps Mark understands something I dont. I think relations that can be viewed as child of and parent of in a hierarchy of categories are extremely important (for reasons set forth in more detail below) and it is not clear to me that Pei meant something other than this. If Mark or anyone else has reason to believe that what [Pei] means is quite different than such child of and parent of relations, I would appreciate being illuminated by what that different meaning is. My understanding of NARS is that it is concerned with inheritance relations, which as I understand it, indicate the truth value of the assumption that one category falls within another category, where category is broadly defined to included not only what we normally think of as categories, but also relationships, slots in relationships, and categories defined by a sets of one or more properties, attributes, elements, relationships, or slot in relationships. Thus, as I understand it, one can view all inheritance statements as indicating the evidence that one instance or category belongs to, and thus is a child of another category, which includes, and thus can be viewed as a parent of the other. Since inheritance relations are transitive, the resulting hierarchy of categories involves nodes that can be considered ancestors (i.e., parents, parents of parents, etc.) of others and nodes that can be viewed as descendents (children, children of children, etc.) of others. I tend to think of similarity as a sibling relationship under a shared hidden parent category -- based on similar aspects of the siblings extensions and/or intensions. In much of my own thinking I have thought of such categorization relations as is generalization, in which the parent is the genus, and the child is the species. Generalization is important for many reasons. First, perception is trying to figure which in category or generalization of things, actions, or situations various parts of a current set of sensory information might fit. Secondly, Generalization is important because it is necessary for implication. All those Bayesian probabilities we are used to thinking about such as P(A|B,C), are totally useless unless we have some way of knowing the probability the situation being considered contains a B or C. To do that you
Re: [agi] Do the inference rules of categorical logic make sense?
MessageMost of the discussion I read in Pei's article related to inheritance relations between terms, that operated as subject and predicates in sentences that are inheritance statements, rather than between entire statements, unless the statement was a subject or a predicate of a higher order inheritance statement. So what you are referring to appears to be beyond what I have read. Label the statement I am allowed to drink alcohol as P and the statement I am an adult as Q. P implies Q and Q implies P (assume that age 21 equals adult) --OR-- P is the parent of Q and Q is the parent of P. Label the statement that most ravens are black as R and the statement that this raven is white as S. R affects the probability of S and, to a lesser extent, S affects the probability of R (both in a negative direction) --OR-- R is the parent of S and S is the parent of R (although, realistically, the probability change is so miniscule that you really could argue that this isn't true). NARS's inheritance is the inheritance of influence on the probability values. - Original Message - From: Edward W. Porter To: agi@v2.listbox.com Sent: Tuesday, October 09, 2007 1:12 PM Subject: RE: [agi] Do the inference rules of categorical logic make sense? Mark, Thank you for your reply. I just ate a lunch with too much fat (luckily largely olive oil) in it so, my brain is a little sleepy. If it is not too much trouble could you please map out the inheritance relationships from which one derives how I am allowed to drink alcohol is both a parent and the child of I am an adult. And could you please do the same with how most ravens are balck is both parent and child of this raven is white. Most of the discussion I read in Pei's article related to inheritance relations between terms, that operated as subject and predicates in sentences that are inheritance statements, rather than between entire statemens, unless the statement was a subject or a predicate of a higher order inheritance statement. So what you are referring to appears to be beyond what I have read. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 12:47 PM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Thus, as I understand it, one can view all inheritance statements as indicating the evidence that one instance or category belongs to, and thus is a child of another category, which includes, and thus can be viewed as a parent of the other. Yes, that is inheritance as Pei uses it. But are you comfortable with the fact that I am allowed to drink alcohol is normally both the parent and the child of I am an adult (and vice versa)? How about the fact that most ravens are black is both the parent and child of this raven is white (and vice versa)? Since inheritance relations are transitive, the resulting hierarchy of categories involves nodes that can be considered ancestors (i.e., parents, parents of parents, etc.) of others and nodes that can be viewed as descendents (children, children of children, etc.) of others. And how often do you really want to do this with concepts like the above -- or when the evidence is substantially less than unity? And loops and transitivity are really ugly . . . . NARS really isn't your father's inheritance. - Original Message - From: Edward W. Porter To: agi@v2.listbox.com Sent: Tuesday, October 09, 2007 12:24 PM Subject: RE: [agi] Do the inference rules of categorical logic make sense? RE: (1) THE VALUE OF CHILD OF AND PARENT OF RELATIONS(2) DISCUSSION OF POSSIBLE VALUE IN DISTINGUISHING BETWEEN GENERALIZATIONAL AND COMPOSITIONAL INHERITANCE HIERARCHIES. Re Mark Waser's 10/9/2007 9:46 AM post: Perhaps Mark understands something I don't. I think relations that can be viewed as child of and parent of in a hierarchy of categories are extremely important (for reasons set forth in more detail below) and it is not clear to me that Pei meant something other than this. If Mark or anyone else has reason to believe that what [Pei] means is quite different than such child of and parent of relations, I would appreciate being illuminated by what that different meaning is. My understanding of NARS is that it is concerned with inheritance relations, which as I understand it, indicate the truth value of the assumption that one category falls within another category, where category is broadly defined to included not only what we normally think of as categories, but also relationships, slots in relationships, and categories defined by a sets of one or more properties, attributes, elements
Re: [agi] Do the inference rules of categorical logic make sense?
On Sun, Oct 07, 2007 at 12:36:10PM -0700, Charles D Hixson wrote: Edward W. Porter wrote: Fred is a human Fred is an animal You REALLY can't do good reasoning using formal logic in natural language...at least in English. That's why the invention of symbolic logic was so important. I suppose this was pounded to death in the rest of the thread, (which I haven't read) but still: syllogistic reasoning does occur in hypothesis formation, and thus, learning: -- maybe humans are animals? What evidence do I have to support this? -- maybe animals are human? Can that be? If Fred has an artificial heart, then perhaps he isn't simply just a special case of an animal. If some pig has human organs in it, then perhaps its an animal that is human. Neither syllogistic deduction is purely false in the real world; there is an it depends aspect to it. learning AI would chalk it up as a maybe, and see is this reasoning leads anywhere. I beleive Pei Wang's NARS system tries to do this; it seems more structured than the fuzzy logic type approaches that antedate it. --linas - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51598751-972d92
RE: [agi] Do the inference rules of categorical logic make sense?
Mark, The basic inference rules in NARS that would support an implication of the form S is a child of P are of the form: DEDUCTION INFERENCE RULE: Given S -- M and M-- P, this implies S -- P ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree where -- is the inheritance relations. Your arguments, are of the very different form : Given P and Q, this implies Q -- P and P -- Q And Given S and R, this implies S -- R and R -- S In the argument regarding drinking and being an adult, you do not appear to use any of these NARS inference rules to show that P inherits from Q or vice versa (unless, perhaps, one assumes multiple other NARS sentences or terms that might help the inference along, such as an uber category such as the category of all categories from which one could use the abduction rule to imply both of the inheritances mentioned (which one would assume the system would have learned over time was such a weak source of implication as to be normally useless). But in that example, just from common sense reasoning, including knowledge of the relevant subject matter, (absent any knowledge of NARS) it appears reasonable to imply P from Q and Q from P. So if NARS did the same it would be behaving in a common sense way. Loops in transitivity might be really ugly, but it seems any human-level AGI has to have the same ability to deal with them as human common sense. To be honest, I do not yet understand how implication is derived from the inheritance relations in NARS. Assuming truth values of one for the child and child/parent inheritance statement, I would guess a child implies its parent with a truth value of one. I would assume a parent with a truth value of one implies a given child with a lesser value that decrease the more often the parent is mapped against other children. The argument claiming NARS says that R (most ravens are black) is both the parent and child of S (this raven is white) (and vice versa), similarly does not appear to be derivable from only the statements given using the NARS inference rules. Nor does my common sense reasoning help me understand why most ravens are black is both the parent and child of this raven is white. (All though my common sense does tell me that this raven is black would provide common sense inductive evidence for most ravens are black and that this raven that is black would be a child of the category of most ravens that are black.) But I do understand that each of these two statements would tend to have probabilistic effects on the other, as you suggested, assuming that the fact a raven is black has implications on whether or not it is white. But such two way probabilistic relationships are at the core of Bayesian inference, so there is no reason why they should not be part of an AGI. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 2:28 PM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Most of the discussion I read in Pei's article related to inheritance relations between terms, that operated as subject and predicates in sentences that are inheritance statements, rather than between entire statements, unless the statement was a subject or a predicate of a higher order inheritance statement. So what you are referring to appears to be beyond what I have read. Label the statement I am allowed to drink alcohol as P and the statement I am an adult as Q. P implies Q and Q implies P (assume that age 21 equals adult) --OR-- P is the parent of Q and Q is the parent of P. Label the statement that most ravens are black as R and the statement that this raven is white as S. R affects the probability of S and, to a lesser extent, S affects the probability of R (both in a negative direction) --OR-- R is the parent of S and S is the parent of R (although, realistically, the probability change is so miniscule that you really could argue that this isn't true). NARS's inheritance is the inheritance of influence on the probability values. - Original Message - From: Edward W. mailto:[EMAIL PROTECTED] Porter To: agi@v2.listbox.com Sent: Tuesday, October 09, 2007 1:12 PM Subject: RE: [agi] Do the inference rules of categorical logic make sense? Mark, Thank you for your reply. I just ate a lunch with too much fat (luckily largely olive oil) in it so, my brain is a little sleepy. If it is not too much trouble could you please map out the inheritance relationships from which one derives how I am allowed to drink alcohol is both a parent and the child of I am an adult. And could you please do the same with how most ravens are balck
Re: [agi] Do the inference rules of categorical logic make sense?
In NARS, the Deduction/Induction/Abduction trio has (at least) three different-though-isomorphic forms, one on inheritance, one on implication, and one mixed. For people who don't have access to the book, see http://nars.wang.googlepages.com/wang.abduction.pdf , though the symbols used in that paper is slightly different from the current form. Pei On 10/9/07, Edward W. Porter [EMAIL PROTECTED] wrote: Mark, The basic inference rules in NARS that would support an implication of the form S is a child of P are of the form: DEDUCTION INFERENCE RULE: Given S -- M and M-- P, this implies S -- P ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree where -- is the inheritance relations. Your arguments, are of the very different form : Given P and Q, this implies Q -- P and P -- Q And Given S and R, this implies S -- R and R -- S In the argument regarding drinking and being an adult, you do not appear to use any of these NARS inference rules to show that P inherits from Q or vice versa (unless, perhaps, one assumes multiple other NARS sentences or terms that might help the inference along, such as an uber category such as the category of all categories from which one could use the abduction rule to imply both of the inheritances mentioned (which one would assume the system would have learned over time was such a weak source of implication as to be normally useless). But in that example, just from common sense reasoning, including knowledge of the relevant subject matter, (absent any knowledge of NARS) it appears reasonable to imply P from Q and Q from P. So if NARS did the same it would be behaving in a common sense way. Loops in transitivity might be really ugly, but it seems any human-level AGI has to have the same ability to deal with them as human common sense. To be honest, I do not yet understand how implication is derived from the inheritance relations in NARS. Assuming truth values of one for the child and child/parent inheritance statement, I would guess a child implies its parent with a truth value of one. I would assume a parent with a truth value of one implies a given child with a lesser value that decrease the more often the parent is mapped against other children. The argument claiming NARS says that R (most ravens are black) is both the parent and child of S (this raven is white) (and vice versa), similarly does not appear to be derivable from only the statements given using the NARS inference rules. Nor does my common sense reasoning help me understand why most ravens are black is both the parent and child of this raven is white. (All though my common sense does tell me that this raven is black would provide common sense inductive evidence for most ravens are black and that this raven that is black would be a child of the category of most ravens that are black.) But I do understand that each of these two statements would tend to have probabilistic effects on the other, as you suggested, assuming that the fact a raven is black has implications on whether or not it is white. But such two way probabilistic relationships are at the core of Bayesian inference, so there is no reason why they should not be part of an AGI. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 2:28 PM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Most of the discussion I read in Pei's article related to inheritance relations between terms, that operated as subject and predicates in sentences that are inheritance statements, rather than between entire statements, unless the statement was a subject or a predicate of a higher order inheritance statement. So what you are referring to appears to be beyond what I have read. Label the statement I am allowed to drink alcohol as P and the statement I am an adult as Q. P implies Q and Q implies P (assume that age 21 equals adult) --OR-- P is the parent of Q and Q is the parent of P. Label the statement that most ravens are black as R and the statement that this raven is white as S. R affects the probability of S and, to a lesser extent, S affects the probability of R (both in a negative direction) --OR-- R is the parent of S and S is the parent of R (although, realistically, the probability change is so miniscule that you really could argue that this isn't true). NARS's inheritance is the inheritance of influence on the probability values. - Original Message - From: Edward W. Porter To: agi@v2.listbox.com Sent: Tuesday, October 09, 2007 1:12 PM Subject: RE: [agi
Re: [agi] Do the inference rules of categorical logic make sense?
, Thomas Serre (Learning a Dictionary of Shape-Components in Visual Cortex: Comparison with Neurons, Humans and Machines, by Thomas Serre, the google-able article I have cited so many times), and many others. Such hierarchical representations achieve their flexibility though a composition/generalization hierarchy which presumably maps easily into NARS. Another key problem in AI is context sensitivity. A hierarchical representation scheme that is capable of computing measures of similarity, fit, and implications throughout multiple levels in such a hierarchical representation scheme of multiple aspects of a situation in real time can be capable of sophisticated real time context sensitivity. In fact, the ability to perform relative extensive real time matching and implication across multiple levels of compositional and generalization hierarchies has been a key feature of the types of systems I have been thinking of for years. That is one of the major reasons why I have argued for BREAKING THE SMALL HARDWARE MINDSET. I understand NARS's inheritance (or categorizations) as being equivalent two both of what I have considered two of the major dimensions in an AGI's self organizing memory, (1) generalization/similarity and (2) composition. I was, however, aware, that down in the compositional (comp) hierarchy can be viewed as up in the generalization (gen) hierarchy, since the set of things having one or more properties or elements of a composition can be viewed as a generalization of that composition (i.e., the generalization covering the category of things having that one or more properties or elements). Although I understand there is an importance equivalence between down in the comp hierarchical and up in the gen hierarchy, and that the two could be viewed as one hierarchy, I have preferred to think of them as different hierarchies, because the type of gens one gets by going up in the gen hierarchy tend to be different than the type of gens one gets by going down in the comp hierarchy. Each possible set in the powerset (the set of all subsets) of elements (eles), relationships (rels), attributes (atts) and contextual patterns (contextual pats) could be considered as possible generalizations. I have assumed, as does Goertzel's Novamente, that there is a competitive ecosystem for representational resources, in which only the fittest pats and gens -- as determined by some measure of usefulness to the system -- survive. There are several major uses of gens, such as aiding in perception, providing inheritance of significant implication, providing appropriate level of representation for learning, and providing invariant representation in higher level comps. Although temporary gens will be generated at a relatively high frequency, somewhat like the inductive implications in NARS, the number of gens that survive and get incorporated into a lot of comps and episodic reps, will be an infinitesimal fraction of the powerset of eles, rels, atts, and contextual features stored in the system. Pats in the up direction in the Gen hierarchy will tend to be ones that have been selected for the usefulness as generalizations. They will often have reasonable number of features that correspond to that of their species node, but with some of them more broadly defined. The gens found by going down in the comp hierarchy are ones that have been selected for their representational value in a comp, and many of them would not normally be that valuable as what we normally think of as generalizations. In the type of system I have been thinking of I have assumed there will be substantially less multiple inheritance in the up direction in the gen hierarchy than in the down direction in the comp hierarchy (in which there would be potential inheritance from every ele, rel, att, and contextual feature of in a comp's descendant nodes at multiple levels in the comp hierarchy below it. Thus, for spreading activation control purposes, I think it is valuable to distinguish between generalization and compositional hierarchies, although I understand they have an important equivalence that should not be ignored. I wonder if NARS makes such a distinction. These are only initial thoughts. I hope to become part of a team that gets an early world-knowledge computing AGI up and running. Perhaps when I do feedback from reality will change my mind. I would welcome comments, not only from Mark, but also from other readers. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 9:46 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? I don't believe that this is the case at all. NARS correctly handles cases where entities co-occur
Re: [agi] Do the inference rules of categorical logic make sense?
In NARS, If A then B is represented as an Implication statement P == Q, whose truth value serves a similar role as P(B|A) in a Bayesian network, though the two have subtle and important differences. For detailed discussion, see http://nars.wang.googlepages.com/wang.bayesianism.pdf and http://nars.wang.googlepages.com/wang.confidence.pdf The Implication relation is isomorphic to the Inheritance relation, but the two are not the same, and cannot exchange with each other. I don't have a short explanation on this topic, so you'd have to read the book, or at least http://nars.wang.googlepages.com/wang.abduction.pdf Pei On 10/9/07, Edward W. Porter [EMAIL PROTECTED] wrote: It wasn't a question to you in particular, but to the list. You had suggested that the terms parent and child were awkward and misleading for probabilistic implication. I was interested in seeing how inheritance statement would represent the types of probabilistic implication most of us are used to thinking in terms of. Bayesian probabilities provide a valuable tool for representation and inference. If one has a probability statement such as p(A|B,C) I understand how NARS's inheritance rules are useful in determining whether you have a B and/or a C, and if you had an A, much of what that would entail. I also understand how they could be used to determine when it would be appropriate for a given perceived or conceived pattern or set of patterns to inherit inferences from other patterns or categories. What I was asking is how categorical logic actually represents the rules of Bayesian inference, and how it derives them from inheritance statements. I was also interested in how the truth values for the existence of B and C, if either or both were less than one, in the above examples, would be blended with the conditional probability of A that p(A|B,C) would imply if the truth values of B and C were one. I might be able to figure this out on my own, but I assume others could do it faster than I, and if somebody has already done it, rather than spending time trying to re-invent the wheel, it would be easier to just read it. I know Novamente has a Probabilistic Term Logic based on both inference from inheritance rules and Bayesian analysis, and I am looking forward to learning more about it, but until that day, perhaps somebody else, such as Pei, has already come up with a mapping between categorical logic and Bayesian probabilities. Ed Porter -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 5:32 PM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? I'm sorry . . . . but I don't understand the question . . . . - Original Message - From: Edward W. Porter To: agi@v2.listbox.com Sent: Tuesday, October 09, 2007 4:57 PM Subject: RE: [agi] Do the inference rules of categorical logic make sense? Mark Waser, With regard to your statement in the below post that my point was meant to be that using the terms parent and child for probabilistic implication is very awkward and misleading, perhaps some one could point out how categorical logic maps into and represents bayesian probabilities (other than the vital role it could play in determining if you have terms corresponding to those in a given Bayesian probability statement---the role Pei was referring to when he said Inference/reasoning is not about to find/prove the absolute truth, but to treat one thing (e.g., a novel object/situation) as another (which is better known in experience)). Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Mark Waser [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 09, 2007 4:25 PM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? To be honest, I do not yet understand how implication is derived from the inheritance relations in NARS. Implication is a form of inheritance. Assuming truth values of one for the child and child/parent inheritance statement, I would guess a child implies its parent with a truth value of one. I would assume a parent with a truth value of one implies a given child with a lesser value that decrease the more often the parent is mapped against other children. A child implies its parent with the frequency of the implication statement. Your arguments, are of the very different form : Given P and Q, this implies Q -- P and P -- Q My apologies. I wasn't even talking about inference rules yet and was unclear. I assumed that you recognized the equivalence of adult and drinking age (i.e. P == Q) and realized that equivalence is exactly the same as two implication statements (P == Q and Q == P). My point was meant to be that using the terms parent and child
Re: [agi] Do the inference rules of categorical logic make sense?
Charles, I fully understand your response --- it is typical when people interpret NARS according to their ideas about how a formal logic should be understood. But NARS is VERY different. Especially, it uses a special semantics, which defines truth and meaning in a way that is fundamentally different from model-theoretic semantics (which is implicitly assumed in your comments everywhere), and I believe is closer to how truth and meaning are treated in natural languages (so you may end up like it). As Mark suggested, you may want to do some reading first (such as http://nars.wang.googlepages.com/wang.semantics.pdf), and after that the discussion will be much more fruitful and efficient. I'm sorry that I don't have a shorter explanation to the related issues. Pei On 10/8/07, Charles D Hixson [EMAIL PROTECTED] wrote: Pei Wang wrote: Charles, What you said is correct for most formal logics formulating binary deduction, using model-theoretic semantics. However, Edward was talking about the categorical logic of NARS, though he put the statements in English, and omitted the truth values, which may caused some misunderstanding. Pei On 10/7/07, Charles D Hixson [EMAIL PROTECTED] wrote: Edward W. Porter wrote: So is the following understanding correct? If you have two statements Fred is a human Fred is an animal And assuming you know nothing more about any of the three terms in both these statements, then each of the following would be an appropriate induction A human is an animal An animal is a human A human and an animal are similar It would only then be from further information that you would find the first of these two inductions has a larger truth value than the second and that the third probably has a larger truth value than the second.. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] Actually, you know less than you have implied. You know that there exists an entity referred to as Fred, and that this entity is a member of both the set human and the set animal. You aren't justified in concluding that any other member of the set human is also a member of the set animal. And conversely. And the only argument for similarity is that the intersection isn't empty. E.g.: Fred is a possessor of purple hair. (He dyed his hair) Fred is a possessor of jellyfish DNA. (He was a subject in a molecular biology experiment. His skin would glow green under proper stimulation.) Now admittedly these sentences would usually be said in a different form (i.e., Fred has green hair), but they are reasonable translations of an equivalent sentence (Fred is a member of the set of people with green hair). You REALLY can't do good reasoning using formal logic in natural language...at least in English. That's why the invention of symbolic logic was so important. If you want to use the old form of syllogism, then at least one of the sentences needs to have either an existential or universal quantifier. Otherwise it isn't a syllogism, but just a pair of statements. And all that you can conclude from them is that they have been asserted. (If they're directly contradictory, then you may question the reliability of the asserter...but that's tricky, as often things that appear to be contradictions actually aren't.) Of course, what this really means is that logic is unsuited for conversation... but it also implies that you shouldn't program your rule-sets in natural language. You'll almost certainly either get them wrong or be ambiguous. (Ambiguity is more common, but it's not exclusive of wrong.) Well, truth values would allow one to assign probabilities to the various statements (i.e., the proffered values plus some uncertainty), but he specifically said we didn't know anything else about the terms, so I don't see how one can go any further. If you don't know what a human is, then knowing that Fred is one doesn't tell you anything about his other characteristics. So when you have two statements about Fred, you know the two statements, but you don't know anything about the relationship between them except that their intersection is non-empty. Since it was specified that we didn't know anything about them, Fred could be a line, and human could be vertical lines and animal could be named entities. For fancier forms of logic (induction, deduction, etc.) you need to have more information. Most forms require that there be at least a partial ordering available, if not several. Many modes of reasoning require that a complete ordering be available. (It doesn't need to be an
Re: [agi] Do the inference rules of categorical logic make sense?
OK. I've read the paper, and don't see where I've made any errors. It looks to me as if NARS can be modeled by a prototype based language with operators for is an ancestor of and is a descendant of. I do have trouble with the language terms that you use, though admittedly they appear to be standard for logicians (to the extent that I'm familiar with their dialect). That might well not be a good implementation, but it appears to be a reasonable model. To me a model can well be dynamic and experience based. In fact I wouldn't consider a model very intelligent if it didn't either itself adapt itself to experience, or it weren't embedded in a matrix which adapted it to experiences. (This doesn't seem to be quite the same meaning that you use for model. Your separation of the rules of inference, the rational faculty, and the model as a fixed and unchanging condition don't match my use of the term. I might pull out the rules of inference as separate pieces and stick them into a datafile, but datafiles can be changed, if anything, more readily than programs...and programs are readily changeable. To me it appears clear that much of the language would need to be interpretive rather than compiled. One should pre-compile what one can for the sake of efficiency, but with the knowledge that this sacrifices flexibility for speed. I still find that I am forced to interpret the inheritance relationship as a is a child of relationship. And I find the idea of continually calculating the powerset of inheritance relationships unappealing. There may not be a better way, but if there isn't, than AGI can't move forwards without vastly more powerful machines. Probably, however, the calculations could be shortcut by increasing the local storage a bit. If each node maintained a list of parents and children, and a count of descendants and ancestors it might suffice. This would increase storage requirements, but drastically cut calculation and still enable the calculation of confidence. Updating the counts could be saved for dreamtime. This would imply that during the early part of learning sleep would be a frequent necessity...but it should become less necessary as the ratio of extant knowledge to new knowledge learned increased. (Note that in this case the amount of new knowledge would be a measured quantity, not an arbitrary constant.) I do feel that the limited sensory modality of the environment (i.e., reading the keyboard) makes AGI unlikely to be feasible. It seems to me that one of the necessary components of true intelligence is integrating multi-modal sensory experience. This doesn't necessarily mean vision and touch, but SOMETHING. As such I can see NARS (or some similar system) as a component of an AGI, but not as a core component (if such exists). OTOH, it might develop into something that would exhibit consciousness. But note that consciousness appears to be primarily an evaluative function rather than a decision making component. It logs and evaluates decisions that have been made, and maintains a delusion that it made them, but they are actually made by other processes, whose nature is less obvious. (It may not actually evaluate them, but I haven't heard of any evidence to justify denying that, and it's certainly a good delusion. Still, were I to wager, I'd wager that it was basically a logging function, and that the evaluations were also made by other processes.) Consciousness appears to have developed to handle those functions that required serialization...and when language came along, it appeared in consciousness, because the limited bandwidth available necessitated serial conversion. Pei Wang wrote: Charles, I fully understand your response --- it is typical when people interpret NARS according to their ideas about how a formal logic should be understood. But NARS is VERY different. Especially, it uses a special semantics, which defines truth and meaning in a way that is fundamentally different from model-theoretic semantics (which is implicitly assumed in your comments everywhere), and I believe is closer to how truth and meaning are treated in natural languages (so you may end up like it). As Mark suggested, you may want to do some reading first (such as http://nars.wang.googlepages.com/wang.semantics.pdf), and after that the discussion will be much more fruitful and efficient. I'm sorry that I don't have a shorter explanation to the related issues. Pei On 10/8/07, Charles D Hixson [EMAIL PROTECTED] wrote: Pei Wang wrote: Charles, What you said is correct for most formal logics formulating binary deduction, using model-theoretic semantics. However, Edward was talking about the categorical logic of NARS, though he put the statements in English, and omitted the truth values, which may caused some misunderstanding. Pei On 10/7/07, Charles D Hixson [EMAIL PROTECTED] wrote: Edward W. Porter wrote:
Re: [agi] Do the inference rules of categorical logic make sense?
Charles, In experience-based learning there are two main problems relating to knowledge acquisition: you have to come up with hypotheses and you have to assess their plausibility. Theoretically, you can regard all hypotheses, but you can't actually do it explicitly because of combinatorial explosion. Instead you create them based on various heuristics. Assessment of plausibility also can't be based on proof most of the time, as new knowledge isn't analytic, it asserts something about the future even though future hasn't happened yet. So, various assessments of plausibility based on usefulness or support by evidence need to be kept track of. As those 'theories' are not limited to explicit language-level statements, they cumulatively can provide all needed facets of meaning. -- Vladimir Nesovmailto:[EMAIL PROTECTED] - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51282587-5eb9f7
Re: [agi] Do the inference rules of categorical logic make sense?
Charles, To be concrete, let me summarize the assumptions in your previous comments, and briefly explain why they don't apply to NARS. *. The meaning of Fred is an entity referred to by the term --- in NARS, the meaning of a term is its relations with other terms (according to the system's experience), not an outside entity. *. The meaning of human and animal are sets of entities --- in NARS, once again the meaning of these terms are determined by their experienced relation with other terms, not sets of outside entities. *. The is a relation (as in Fred is a human) is represented as membership relation in set theory --- in NARS, it is an inheritance relation with experience-based truth value. *. The truth value of a statement measures whether, or how much, the statement matches the corresponding fact (you didn't say so explicitly, but it is implied by your comments about INDUCTION and ABDUCTION) --- in NARS, as you have read in my paper, truth value measures evidential support, that is, how much a statement matches what the system knows, not the world as it is. Now let's see Edward's example for induction: from Fred is a human and Fred is an animal to derive A human is an animal and An animal is a human (truth values omitted). You said Actually, you know less than you have implied. You know that there exists an entity referred to as Fred, and that this entity is a member of both the set human and the set animal. You aren't justified in concluding that any other member of the set human is also a member of the set animal. And conversely. which is correct deduction according to a model-theoretic interpretation of the statements. However, under the experience-grounded semantics, the NARS conclusions don't state that the two sets human and animal, as we know them, includes each other --- that cannot be derived, even in a probabilistic sense. Instead, they states that the two concepts, human and animal, as the system know them, can substitute each other, in certain way and to certain extent. An intelligent system will use this kind of inference to predict the future (such as to expect the next time human is used as a predicate term, it can be replaced by animal), so as to go beyond the scope of binary deduction. Such predictions can turn out to be wrong, but I believe this is how adaptation/intelligence works. For now I won't comment on the other issues in your following message --- there are too many of them. Instead, I hope to make myself clear on the basic topics first. Pei On 10/8/07, Charles D Hixson [EMAIL PROTECTED] wrote: OK. I've read the paper, and don't see where I've made any errors. It looks to me as if NARS can be modeled by a prototype based language with operators for is an ancestor of and is a descendant of. I do have trouble with the language terms that you use, though admittedly they appear to be standard for logicians (to the extent that I'm familiar with their dialect). That might well not be a good implementation, but it appears to be a reasonable model. To me a model can well be dynamic and experience based. In fact I wouldn't consider a model very intelligent if it didn't either itself adapt itself to experience, or it weren't embedded in a matrix which adapted it to experiences. (This doesn't seem to be quite the same meaning that you use for model. Your separation of the rules of inference, the rational faculty, and the model as a fixed and unchanging condition don't match my use of the term. I might pull out the rules of inference as separate pieces and stick them into a datafile, but datafiles can be changed, if anything, more readily than programs...and programs are readily changeable. To me it appears clear that much of the language would need to be interpretive rather than compiled. One should pre-compile what one can for the sake of efficiency, but with the knowledge that this sacrifices flexibility for speed. I still find that I am forced to interpret the inheritance relationship as a is a child of relationship. And I find the idea of continually calculating the powerset of inheritance relationships unappealing. There may not be a better way, but if there isn't, than AGI can't move forwards without vastly more powerful machines. Probably, however, the calculations could be shortcut by increasing the local storage a bit. If each node maintained a list of parents and children, and a count of descendants and ancestors it might suffice. This would increase storage requirements, but drastically cut calculation and still enable the calculation of confidence. Updating the counts could be saved for dreamtime. This would imply that during the early part of learning sleep would be a frequent necessity...but it should become less necessary as the ratio of extant knowledge to new knowledge learned increased. (Note that in this case the amount of new knowledge would be a measured quantity, not an arbitrary constant.) I
RE: [agi] Do the inference rules of categorical logic make sense?
Charles D. Hixsons post of 10/8/2007 5:50 PM, was quite impressive as a first reaction upon reading about NARS. After I first read Pei Wangs A Logic of Categorization, it took me quite a while to know what I thought of it. It was not until I got answers to some of my basic questions from Pei though postings under the current thread title that I was able to start to understand it reasonably well. Since then I have been coming to understand that it is quite similar to some of my own previous thinking, and if it were used in a certain way, it would seem to have tremendous potential. But I still have some questions about it, such as (PEI, IF YOU ARE READING THIS I WOULD BE INTERESTED IN HEARING YOUR ANSWERS) --(1) How are episodes represented in NARS? --(2) How are complex pattern and sets of patterns with many interrelated elements represented in NARS? (I.e., how would NARS represents an auto mechanics understanding of automobiles? Would it be in terms of many thousands of sentences containing relational inheritance statements such as those shown on page 197 of A Logic of Categorization?) --(3) How are time and temporal patterns represented? --(4) How are specific mappings between the elements of a pattern and what they map to represented in NARS? --(5) How does NARS learn behaviors? --(6) Finally, this is a much larger question. Is it really optimal to limit your representational scheme to a language in which all sentences are based on the inheritance relation? With regard to Question (6): Categorization is essential. I dont question that. I believe the pattern is the essential source of intelligence. It is essential to implication and reasoning from experiences. NARSs categorization relates to patterns and relationships between patterns. It patterns are represented in a generalization hierarchy (where a property or set of properties can be viewed as a generalization), with a higher level pattern (i.e., category) being able to represent different species of itself in the different contexts where those different species are appropriate, thus, helping to solve two of the major problems in AI, that of non-literal matching and context appropriateness. All this is well and good. But without having had a chance to fully consider the subject it seems to me that there might be other aspects of reality and representation that -- even if they might all be reducible to representation in terms of categorization -- could perhaps be more easily thought of by us poor humans in terms of concepts other than categorization. For example, Novamente bases its inference and much of its learning on PTL, Probabilistic Term Logic, which is based on inheritance relations, much as is NARS. But both of Bens articles on Novamente spend a lot of time describing things in terms like hypergraph, maps, attractors, logical unification, PredicateNodes, genetic programming, and associative links. Yes, perhaps all these things could be thought of as categories, inheritance statements, and things derived from them of the type described in you paper A Logic of Catagorization, and such thoughts might provide valuable insights, but is that the most efficient way for us mortals to think of them and for a machine to represent them. I would be interested in hearing your answer to all these questions. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51300772-e34770
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/8/07, Edward W. Porter [EMAIL PROTECTED] wrote: --(1) How are episodes represented in NARS? As events --- see http://nars.wang.googlepages.com/wang.roadmap.pdf , pages 7-8 --(2) How are complex pattern and sets of patterns with many interrelated elements represented in NARS? (I.e., how would NARS represents an auto mechanic's understanding of automobiles? Would it be in terms of many thousands of sentences containing relational inheritance statements such as those shown on page 197 of A Logic of Categorization?) Not necessarily inheritance statements, but Narsese statements in general. --(3) How are time and temporal patterns represented? As events or operations --- again, see http://nars.wang.googlepages.com/wang.roadmap.pdf , pages 7-8 --(4) How are specific mappings between the elements of a pattern and what they map to represented in NARS? As various types of relation, which are special type of term. --(5) How does NARS learn behaviors? Mainly through procedural reasoning --- the above paper has a brief description, and the book has a more detailed description, though I'm still working on the details. --(6) Finally, this is a much larger question. Is it really optimal to limit your representational scheme to a language in which all sentences are based on the inheritance relation? Well, it indeed deserves a longer answer. First, NARS doesn't use the inheritance relation for all sentences --- in the current implementation, there are four relations in the memory: inheritance, similarity, implication, and equivalence. Though the later three are derived from inheritance conceptually, they are processed on their own. Second, to say the memory contains four basic relation types doesn't prevent the system from representing and processing other user-defined relations --- see the above paper, page 5, Products and Images. It is just that only the four basic types have fixed meaning, while the meaning of the other relations are learned from experience. With regard to Question (6): Categorization is essential. I don't question that. I believe the pattern is the essential source of intelligence. It is essential to implication and reasoning from experiences. NARS's categorization relates to patterns and relationships between patterns. It patterns are represented in a generalization hierarchy (where a property or set of properties can be viewed as a generalization), with a higher level pattern (i.e., category) being able to represent different species of itself in the different contexts where those different species are appropriate, thus, helping to solve two of the major problems in AI, that of non-literal matching and context appropriateness. All this is well and good. But without having had a chance to fully consider the subject it seems to me that there might be other aspects of reality and representation that -- even if they might all be reducible to representation in terms of categorization -- could perhaps be more easily thought of by us poor humans in terms of concepts other than categorization. NARS doesn't rule out problem-specific and domain-specific representation, though they are handled at a different level. Narsese is like the native language of NARS, though based on it the system can learn various types of second/foreign languages (including natural languages). However, this is different from merging those languages into Narsese. See the above paper, pages 9-10, Natural languages, for a brief explanation. For example, Novamente bases its inference and much of its learning on PTL, Probabilistic Term Logic, which is based on inheritance relations, much as is NARS. But both of Ben's articles on Novamente spend a lot of time describing things in terms like hypergraph, maps, attractors, logical unification, PredicateNodes, genetic programming, and associative links. Yes, perhaps all these things could be thought of as categories, inheritance statements, and things derived from them of the type described in you paper A Logic of Catagorization, and such thoughts might provide valuable insights, but is that the most efficient way for us mortals to think of them and for a machine to represent them. NARS and Novamente surely still have some family resemblance left --- for a family story, read http://www.goertzel.org/benzine/WakingUpFromTheEconomyOfDreams.htm These two systems have many similarities, as well as important differences, on which I and Ben have debated for years. It is too big a topic to be addressed here. Pei - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51308317-fadbbc
Re: [agi] Do the inference rules of categorical logic make sense?
Mike Tintner wrote: Vladimir: In experience-based learning there are two main problems relating to knowledge acquisition: you have to come up with hypotheses and you have to assess their plausibility. ...you create them based on various heuristics. How is this different from narrow AI? It seems like narrow AI - does Nars have the ability to learn unprogrammed, or invent, totally new kinds of logic? Or kinds of algebra? In fact, the definitions of Nars: NARS is intelligent in the sense that it is adaptive, and works with insufficient knowledge and resources. By adaptive, we mean that NARS uses its experience (i.e., the history of its interaction with the environment) as the guidance of its inference activities. For each question, it looks for an answer that is most consistent with its experience (under the restriction of available resources). define narrow AI systems - which are also intelligent, adaptive, work with insufficient knowledge and resources and learn from experience. There seems to be nothing in those definitions which is distinctive to AGI. With a sufficient knowledge base, which would require learning, NARS looks as if it could categorize that which it knows about, and make guesses as to how certain pieces of information are related to other pieces of information. An extended version should be adaptive in the patterns that it recognizes. OTOH, I don't recognize any features that would enable it to take independent action, so I suspect that it would be but one module of a more complex system. N.B.: I'm definitely no expert at NARS, I've only read two of the papers a a few arguments. Features that I didn't notice could well be present. And they could certainly be in the planning stage. I'm a bit hesitant about the theoretical framework, as it appears computationally expensive. Still, implementation doesn't necessarily follow theory, and theory can jump over the gnarly bits, leaving them for implementation. It's possible that lazy evaluation and postponed stability calculations could make things a LOT more efficient. These probably aren't practical until the database grows to a reasonable size, however. But as I understand it, this still wouldn't be an AGI, but merely a categorizer. (OTOH, I only read two of the papers. These could just be the papers that cover the categorizer. Plausibly other papers cover other aspects.) N.B.: The current version of NARS, as described, only parses a specialized language covering topics of inheritance of characteristics. As such, that's all that was covered by the paper I most recently read. This doesn't appear to be an inherent limitation, as the terminal nodes are primitive text and, as such, could, in principle, invoke other routines, or refer to the contents of an image. The program would neither know nor care. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51310341-2108b3
Re: [agi] Do the inference rules of categorical logic make sense?
Charles, The computational complexity or resources expense of NARS is another aspect on which this system is fundamentally different from existing systems. I understand that from the inference rules alone, people will think it is too expensive to be actually implemented, simply because there are so many possible ways to make inference. You may want to read http://nars.wang.googlepages.com/wang.computation.pdf to see how the inference processes are controlled in the system. I've commented on the perceived limitation of the inheritance-based language in my comment on Edward. Pei On 10/8/07, Charles D Hixson [EMAIL PROTECTED] wrote: Mike Tintner wrote: Vladimir: In experience-based learning there are two main problems relating to knowledge acquisition: you have to come up with hypotheses and you have to assess their plausibility. ...you create them based on various heuristics. How is this different from narrow AI? It seems like narrow AI - does Nars have the ability to learn unprogrammed, or invent, totally new kinds of logic? Or kinds of algebra? In fact, the definitions of Nars: NARS is intelligent in the sense that it is adaptive, and works with insufficient knowledge and resources. By adaptive, we mean that NARS uses its experience (i.e., the history of its interaction with the environment) as the guidance of its inference activities. For each question, it looks for an answer that is most consistent with its experience (under the restriction of available resources). define narrow AI systems - which are also intelligent, adaptive, work with insufficient knowledge and resources and learn from experience. There seems to be nothing in those definitions which is distinctive to AGI. With a sufficient knowledge base, which would require learning, NARS looks as if it could categorize that which it knows about, and make guesses as to how certain pieces of information are related to other pieces of information. An extended version should be adaptive in the patterns that it recognizes. OTOH, I don't recognize any features that would enable it to take independent action, so I suspect that it would be but one module of a more complex system. N.B.: I'm definitely no expert at NARS, I've only read two of the papers a a few arguments. Features that I didn't notice could well be present. And they could certainly be in the planning stage. I'm a bit hesitant about the theoretical framework, as it appears computationally expensive. Still, implementation doesn't necessarily follow theory, and theory can jump over the gnarly bits, leaving them for implementation. It's possible that lazy evaluation and postponed stability calculations could make things a LOT more efficient. These probably aren't practical until the database grows to a reasonable size, however. But as I understand it, this still wouldn't be an AGI, but merely a categorizer. (OTOH, I only read two of the papers. These could just be the papers that cover the categorizer. Plausibly other papers cover other aspects.) N.B.: The current version of NARS, as described, only parses a specialized language covering topics of inheritance of characteristics. As such, that's all that was covered by the paper I most recently read. This doesn't appear to be an inherent limitation, as the terminal nodes are primitive text and, as such, could, in principle, invoke other routines, or refer to the contents of an image. The program would neither know nor care. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=51312250-bbbc49
Re: [agi] Do the inference rules of categorical logic make sense?
Edward W. Porter wrote: So is the following understanding correct? If you have two statements Fred is a human Fred is an animal And assuming you know nothing more about any of the three terms in both these statements, then each of the following would be an appropriate induction A human is an animal An animal is a human A human and an animal are similar It would only then be from further information that you would find the first of these two inductions has a larger truth value than the second and that the third probably has a larger truth value than the second.. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] Actually, you know less than you have implied. You know that there exists an entity referred to as Fred, and that this entity is a member of both the set human and the set animal. You aren't justified in concluding that any other member of the set human is also a member of the set animal. And conversely. And the only argument for similarity is that the intersection isn't empty. E.g.: Fred is a possessor of purple hair. (He dyed his hair) Fred is a possessor of jellyfish DNA. (He was a subject in a molecular biology experiment. His skin would glow green under proper stimulation.) Now admittedly these sentences would usually be said in a different form (i.e., Fred has green hair), but they are reasonable translations of an equivalent sentence (Fred is a member of the set of people with green hair). You REALLY can't do good reasoning using formal logic in natural language...at least in English. That's why the invention of symbolic logic was so important. If you want to use the old form of syllogism, then at least one of the sentences needs to have either an existential or universal quantifier. Otherwise it isn't a syllogism, but just a pair of statements. And all that you can conclude from them is that they have been asserted. (If they're directly contradictory, then you may question the reliability of the asserter...but that's tricky, as often things that appear to be contradictions actually aren't.) Of course, what this really means is that logic is unsuited for conversation... but it also implies that you shouldn't program your rule-sets in natural language. You'll almost certainly either get them wrong or be ambiguous. (Ambiguity is more common, but it's not exclusive of wrong.) - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50932465-797f53
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/7/07, Charles D Hixson [EMAIL PROTECTED] wrote: ... logic is unsuited for conversation... what a great quote - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50946633-33f0fb
Re: [agi] Do the inference rules of categorical logic make sense?
Charles, What you said is correct for most formal logics formulating binary deduction, using model-theoretic semantics. However, Edward was talking about the categorical logic of NARS, though he put the statements in English, and omitted the truth values, which may caused some misunderstanding. Pei On 10/7/07, Charles D Hixson [EMAIL PROTECTED] wrote: Edward W. Porter wrote: So is the following understanding correct? If you have two statements Fred is a human Fred is an animal And assuming you know nothing more about any of the three terms in both these statements, then each of the following would be an appropriate induction A human is an animal An animal is a human A human and an animal are similar It would only then be from further information that you would find the first of these two inductions has a larger truth value than the second and that the third probably has a larger truth value than the second.. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] Actually, you know less than you have implied. You know that there exists an entity referred to as Fred, and that this entity is a member of both the set human and the set animal. You aren't justified in concluding that any other member of the set human is also a member of the set animal. And conversely. And the only argument for similarity is that the intersection isn't empty. E.g.: Fred is a possessor of purple hair. (He dyed his hair) Fred is a possessor of jellyfish DNA. (He was a subject in a molecular biology experiment. His skin would glow green under proper stimulation.) Now admittedly these sentences would usually be said in a different form (i.e., Fred has green hair), but they are reasonable translations of an equivalent sentence (Fred is a member of the set of people with green hair). You REALLY can't do good reasoning using formal logic in natural language...at least in English. That's why the invention of symbolic logic was so important. If you want to use the old form of syllogism, then at least one of the sentences needs to have either an existential or universal quantifier. Otherwise it isn't a syllogism, but just a pair of statements. And all that you can conclude from them is that they have been asserted. (If they're directly contradictory, then you may question the reliability of the asserter...but that's tricky, as often things that appear to be contradictions actually aren't.) Of course, what this really means is that logic is unsuited for conversation... but it also implies that you shouldn't program your rule-sets in natural language. You'll almost certainly either get them wrong or be ambiguous. (Ambiguity is more common, but it's not exclusive of wrong.) - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50965360-951ab5
Re: [agi] Do the inference rules of categorical logic make sense?
Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50749379-2a7926
Re: [agi] Do the inference rules of categorical logic make sense?
Right. See concrete examples in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt In induction and abduction, S--P and P--S are usually (though not always) produced in pair, though usually (though not always) with different truth values, unless the two premises have the same truth-value --- as Edward said, it would be illogical to produce difference from sameness. ;-) Especially, positive evidence equally support both conclusions, while negative evidence only deny one of the two --- see the Induction and Revision example in http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt For a more focused discussion on induction in NARS, see http://www.cogsci.indiana.edu/pub/wang.induction.ps The situation for S-P is similar --- see comparison in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt Pei On 10/6/07, Lukasz Stafiniak [EMAIL PROTECTED] wrote: Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50765665-44f7f5
RE: [agi] Do the inference rules of categorical logic make sense?
If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50766573-29b233
RE: [agi] Do the inference rules of categorical logic make sense?
So is the following understanding correct? If you have two statements Fred is a human Fred is an animal And assuming you know nothing more about any of the three terms in both these statements, then each of the following would be an appropriate induction A human is an animal An animal is a human A human and an animal are similar It would only then be from further information that you would find the first of these two inductions has a larger truth value than the second and that the third probably has a larger truth value than the second.. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 7:03 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Right. See concrete examples in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt In induction and abduction, S--P and P--S are usually (though not always) produced in pair, though usually (though not always) with different truth values, unless the two premises have the same truth-value --- as Edward said, it would be illogical to produce difference from sameness. ;-) Especially, positive evidence equally support both conclusions, while negative evidence only deny one of the two --- see the Induction and Revision example in http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt For a more focused discussion on induction in NARS, see http://www.cogsci.indiana.edu/pub/wang.induction.ps The situation for S-P is similar --- see comparison in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt Pei On 10/6/07, Lukasz Stafiniak [EMAIL PROTECTED] wrote: Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50767228-6b318e
Re: [agi] Do the inference rules of categorical logic make sense?
The order here isn't the incoming order of the premises. From M--S(t1) and M--P(t2), where t1 and t2 are truth values, the rule produces two symmetric conclusions, and which truth function is called depends on the subject/predicate order in the conclusion. That is, S--P will use a function f(t1,t2), while P--S will use the symmetric function f(t2,t1). Pei On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50767869-3791d3
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: So is the following understanding correct? If you have two statements Fred is a human Fred is an animal And assuming you know nothing more about any of the three terms in both these statements, then each of the following would be an appropriate induction A human is an animal An animal is a human A human and an animal are similar Correct, though for technical reasons I don't call the last one induction but comparison. It would only then be from further information that you would find the first of these two inductions has a larger truth value than the second and that the third probably has a larger truth value than the second.. Right, though the rules immediately assigns truth values to the conclusion, based on the evidence provided by the current premises. The role of further information is to revise the previous truth values. In this way, the system can always form a belief (rather than waiting for enough information), though the initial beliefs will have low confidence. Pei Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 7:03 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Right. See concrete examples in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt In induction and abduction, S--P and P--S are usually (though not always) produced in pair, though usually (though not always) with different truth values, unless the two premises have the same truth-value --- as Edward said, it would be illogical to produce difference from sameness. ;-) Especially, positive evidence equally support both conclusions, while negative evidence only deny one of the two --- see the Induction and Revision example in http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt For a more focused discussion on induction in NARS, see http://www.cogsci.indiana.edu/pub/wang.induction.ps The situation for S-P is similar --- see comparison in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt Pei On 10/6/07, Lukasz Stafiniak [EMAIL PROTECTED] wrote: Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50768597-1784af
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Pei Wang [EMAIL PROTECTED] wrote:
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote:
So is the following understanding correct?
If you have two statements
Fred is a human
Fred is an animal
And assuming you know nothing more about any of the three terms in both
these statements, then each of the following would be an appropriate
induction
A human is an animal
An animal is a human
A human and an animal are similar
Correct, though for technical reasons I don't call the last one
induction but comparison.
BTW, in the future you can easily try it yourself, if you want:
(1) start the NARS demo by clicking http://nars.wang.googlepages.com/NARS.html
(2) open the inference log window by select View/Inference Log from
the main window
(3) copy/paste the following two lines into the input window:
Fred {-- human.
Fred {-- animal.
then click OK.
(4) click Walk in the main window for a few times. For this example,
in the 5th step the three conclusions you mentioned will be produced,
with a bunch of others.
There is a User's Guide for the demo at
http://nars.wang.googlepages.com/NARS-Guide.html
Pei
-
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To unsubscribe or change your options, please go to:
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RE: [agi] Do the inference rules of categorical logic make sense?
Thanks. So as I understand it, whether a premise is major or minor is defined by its role of its terms relative to a given conconclusion. But the same premise could play a major role relative to once conclusion and a minor role relative to another. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 8:20 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? The order here isn't the incoming order of the premises. From M--S(t1) and M--P(t2), where t1 and t2 are truth values, the rule produces two symmetric conclusions, and which truth function is called depends on the subject/predicate order in the conclusion. That is, S--P will use a function f(t1,t2), while P--S will use the symmetric function f(t2,t1). Pei On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50771155-cc051f
RE: [agi] Do the inference rules of categorical logic make sense?
Great, I look forward to trying this when I get back from a brief
vacation for the holiday weekend.
Edward W. Porter
Porter Associates
24 String Bridge S12
Exeter, NH 03833
(617) 494-1722
Fax (617) 494-1822
[EMAIL PROTECTED]
-Original Message-
From: Pei Wang [mailto:[EMAIL PROTECTED]
Sent: Saturday, October 06, 2007 8:51 AM
To: agi@v2.listbox.com
Subject: Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Pei Wang [EMAIL PROTECTED] wrote:
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote:
So is the following understanding correct?
If you have two statements
Fred is a human
Fred is an animal
And assuming you know nothing more about any of the three terms in
both these statements, then each of the following would be an
appropriate induction
A human is an animal
An animal is a human
A human and an animal are similar
Correct, though for technical reasons I don't call the last one
induction but comparison.
BTW, in the future you can easily try it yourself, if you want:
(1) start the NARS demo by clicking
http://nars.wang.googlepages.com/NARS.html
(2) open the inference log window by select View/Inference Log from the
main window
(3) copy/paste the following two lines into the input window:
Fred {-- human.
Fred {-- animal.
then click OK.
(4) click Walk in the main window for a few times. For this example, in
the 5th step the three conclusions you mentioned will be produced, with a
bunch of others.
There is a User's Guide for the demo at
http://nars.wang.googlepages.com/NARS-Guide.html
Pei
-
This list is sponsored by AGIRI: http://www.agiri.org/email
To unsubscribe or change your options, please go to:
http://v2.listbox.com/member/?;
-
This list is sponsored by AGIRI: http://www.agiri.org/email
To unsubscribe or change your options, please go to:
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Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: Thanks. So as I understand it, whether a premise is major or minor is defined by its role of its terms relative to a given conconclusion. But the same premise could play a major role relative to once conclusion and a minor role relative to another. Exactly (though I usually don't use the terms major and minor). Furthermore, the same belief can be used as premise in various types of inference (deduction, induction, abduction, comparison, analogy, revision, ...), and plays different roles in each of them. Pei Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 8:20 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? The order here isn't the incoming order of the premises. From M--S(t1) and M--P(t2), where t1 and t2 are truth values, the rule produces two symmetric conclusions, and which truth function is called depends on the subject/predicate order in the conclusion. That is, S--P will use a function f(t1,t2), while P--S will use the symmetric function f(t2,t1). Pei On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50771875-8eff2f
[agi] Do the inference rules of categorical logic make sense?
I am trying to understand categorical logic from reading Pei Wangs very interesting paper, A Logic of Categorization. Since I am a total newbie to the field I have some probably dumb questions. But at the risk of making a fool of myself let me ask them to members of the list. Lets use -- as the arrow symbol commonly used to represent an inheritance relation of the type used in categorical logic, where A -- B, roughly means category A is a species (or instance) of category B. Category B, in addition to what we might normally think as a generalization, can also be a property (meaning Bs category would be that of concepts having property B). I understand how the deduction inference rule works. DEDUCTION INFERENCE RULE: Given S -- M and M-- P, this implies S -- P This make total sense. If S is a type of M, and M is a type of P, S is a type of P. But I dont understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. It would appear to me that both the Abduction and Induction inference rules should imply each of the following, each with some degree of evidentiary value S -- P P -- S, and S -- P, where -- represents a similarity relation. Since these rules have been around for years I assume the rules are right and my understanding is wrong. I would appreciate it if someone on the list with more knowledge of the subject than I could point out my presumed error. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50726265-cee19c
