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: [email protected] 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. 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: [email protected] 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/?&; ----- 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=8660244&id_secret=51488069-dbdf5f
