Re: [agi] two types of semantics [Was: NARS and probability]
Thanks Pei, I would add (for others, obviously you know this stuff) that there are many different theoretical justifications of probability theory, hence that the use of probability theory does not imply model-theoretic semantics nor any other particular approach to semantics. My own philosophy is even further from your summary of model-theoretic semantics than it is from (my reading of) Tarski's original version of model theoretic semantics. I am not an objectivist whatsoever (I read too many Oriental philosophy books in my early youth, when my mom was studying for her PhD in Chinese history, and my brain was even more pliant ;-). I deal extensively with objectivity/subjectivity/intersubjectivity issues in The Hidden Pattern. As an example, if one justifies probability theory according a Cox's-axioms approach, no model theory is necessary. In this approach, it is justified as a set of a priori constraints that the system chooses to impose on its own reasoning. In a de Finetti approach, it is justified because the system wants to be able to win bets with other agents. The intersection between this notion and the hypothesis of an objective world is unclear, but it's not obvious why these hypothetical agents need to have objective existence. As you say, this is a deep philosophical rat's-nest... my point is just that it's not correct to imply probability theory = traditional model theoretic semantics -- Ben G On Sun, Oct 12, 2008 at 8:29 AM, Pei Wang [EMAIL PROTECTED] wrote: A brief and non-technical description of the two types of semantics mentioned in the previous discussions: (1) Model-Theoretic Semantics (MTS) (1.1) There is a world existing independently outside the intelligent system (human or machine). (1.2) In principle, there is an objective description of the world, in terms of objects, their properties, and relations among them. (1.3) Within the intelligent system, its knowledge is an approximation of the objective description of the world. (1.4) The meaning of a symbol within the system is the object it refers to in the world. (1.5) The truth-value of a statement within the system measures how close it approximates the fact in the world. (2) Experience-Grounded Semantics (EGS) (2.1) There is a world existing independently outside the intelligent system (human or machine). [same as (1.1), but the agreement stops here] (2.2) Even in principle, there is no objective description of the world. What the system has is its experience, the history of its interaction of the world. (2.3) Within the intelligent system, its knowledge is a summary of its experience. (2.4) The meaning of a symbol within the system is determined by its role in the experience. (2.5) The truth-value of a statement within the system measures how close it summarizes the relevant part of the experience. To further simplify the description, in the context of learning and reasoning: MTS takes objective truth of statements and real meaning of terms as aim of approximation, while EGS refuses them, but takes experience (input data) as the only thing to depend on. As usual, each theory has its strength and limitation. The issue is which one is more proper for AGI. MTS has been dominating in math, logic, and computer science, and therefore is accepted by the majority people. Even so, it has been attacked by other people (not only the EGS believers) for many reasons. A while ago I made a figure to illustrate this difference, which is at http://nars.wang.googlepages.com/wang.semantics-figure.pdf . A manifesto of EGS is at http://nars.wang.googlepages.com/wang.semantics.pdf Since the debate on the nature of truth and meaning has existed for thousands of years, I don't think we can settle down it here by some email exchanges. I just want to let the interested people know the theoretical background of the related discussions. Pei On Sat, Oct 11, 2008 at 8:34 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly the difference between an experience-grounded semantics and a model-theoretic semantics. I don't agree with this distinction ... unless you are construing model theoretic semantics in a very restrictive way, which then does not apply to PLN. If by model-theoretic semantics you mean something like what Wikipedia says at http://en.wikipedia.org/wiki/Formal_semantics, *** Model-theoretic semantics is the archetype of Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of model theory. This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by
Re: [agi] two types of semantics [Was: NARS and probability]
Ben, Of course, probability theory, in its mathematical form, is not bounded to any semantics at all, though it implicitly exclude some possibilities. A semantic theory is associated to it when probability theory is applied to a practical situation. There are several major schools in the interpretation of probability (see http://plato.stanford.edu/entries/probability-interpret/), and their relations with NARS is explained in Section 8.5.1 of my book. As for the interpretation of probability in PLN, I'd rather wait for your book than to make comment based on your brief explanation. Pei On Sun, Oct 12, 2008 at 9:13 AM, Ben Goertzel [EMAIL PROTECTED] wrote: Thanks Pei, I would add (for others, obviously you know this stuff) that there are many different theoretical justifications of probability theory, hence that the use of probability theory does not imply model-theoretic semantics nor any other particular approach to semantics. My own philosophy is even further from your summary of model-theoretic semantics than it is from (my reading of) Tarski's original version of model theoretic semantics. I am not an objectivist whatsoever (I read too many Oriental philosophy books in my early youth, when my mom was studying for her PhD in Chinese history, and my brain was even more pliant ;-). I deal extensively with objectivity/subjectivity/intersubjectivity issues in The Hidden Pattern. As an example, if one justifies probability theory according a Cox's-axioms approach, no model theory is necessary. In this approach, it is justified as a set of a priori constraints that the system chooses to impose on its own reasoning. In a de Finetti approach, it is justified because the system wants to be able to win bets with other agents. The intersection between this notion and the hypothesis of an objective world is unclear, but it's not obvious why these hypothetical agents need to have objective existence. As you say, this is a deep philosophical rat's-nest... my point is just that it's not correct to imply probability theory = traditional model theoretic semantics -- Ben G On Sun, Oct 12, 2008 at 8:29 AM, Pei Wang [EMAIL PROTECTED] wrote: A brief and non-technical description of the two types of semantics mentioned in the previous discussions: (1) Model-Theoretic Semantics (MTS) (1.1) There is a world existing independently outside the intelligent system (human or machine). (1.2) In principle, there is an objective description of the world, in terms of objects, their properties, and relations among them. (1.3) Within the intelligent system, its knowledge is an approximation of the objective description of the world. (1.4) The meaning of a symbol within the system is the object it refers to in the world. (1.5) The truth-value of a statement within the system measures how close it approximates the fact in the world. (2) Experience-Grounded Semantics (EGS) (2.1) There is a world existing independently outside the intelligent system (human or machine). [same as (1.1), but the agreement stops here] (2.2) Even in principle, there is no objective description of the world. What the system has is its experience, the history of its interaction of the world. (2.3) Within the intelligent system, its knowledge is a summary of its experience. (2.4) The meaning of a symbol within the system is determined by its role in the experience. (2.5) The truth-value of a statement within the system measures how close it summarizes the relevant part of the experience. To further simplify the description, in the context of learning and reasoning: MTS takes objective truth of statements and real meaning of terms as aim of approximation, while EGS refuses them, but takes experience (input data) as the only thing to depend on. As usual, each theory has its strength and limitation. The issue is which one is more proper for AGI. MTS has been dominating in math, logic, and computer science, and therefore is accepted by the majority people. Even so, it has been attacked by other people (not only the EGS believers) for many reasons. A while ago I made a figure to illustrate this difference, which is at http://nars.wang.googlepages.com/wang.semantics-figure.pdf . A manifesto of EGS is at http://nars.wang.googlepages.com/wang.semantics.pdf Since the debate on the nature of truth and meaning has existed for thousands of years, I don't think we can settle down it here by some email exchanges. I just want to let the interested people know the theoretical background of the related discussions. Pei On Sat, Oct 11, 2008 at 8:34 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly
Re: [agi] two types of semantics [Was: NARS and probability]
Pei, In this context, how do you justify the use of 'k'? It seems like, by introducing 'k', you add a reliance on the truth of the future after k observations into the semantics. Since the induction/abduction formula is dependent on 'k', the truth values that result no longer only summarize experience; they are calculated with prediction in mind. --Abram On Sun, Oct 12, 2008 at 8:29 AM, Pei Wang [EMAIL PROTECTED] wrote: A brief and non-technical description of the two types of semantics mentioned in the previous discussions: (1) Model-Theoretic Semantics (MTS) (1.1) There is a world existing independently outside the intelligent system (human or machine). (1.2) In principle, there is an objective description of the world, in terms of objects, their properties, and relations among them. (1.3) Within the intelligent system, its knowledge is an approximation of the objective description of the world. (1.4) The meaning of a symbol within the system is the object it refers to in the world. (1.5) The truth-value of a statement within the system measures how close it approximates the fact in the world. (2) Experience-Grounded Semantics (EGS) (2.1) There is a world existing independently outside the intelligent system (human or machine). [same as (1.1), but the agreement stops here] (2.2) Even in principle, there is no objective description of the world. What the system has is its experience, the history of its interaction of the world. (2.3) Within the intelligent system, its knowledge is a summary of its experience. (2.4) The meaning of a symbol within the system is determined by its role in the experience. (2.5) The truth-value of a statement within the system measures how close it summarizes the relevant part of the experience. To further simplify the description, in the context of learning and reasoning: MTS takes objective truth of statements and real meaning of terms as aim of approximation, while EGS refuses them, but takes experience (input data) as the only thing to depend on. As usual, each theory has its strength and limitation. The issue is which one is more proper for AGI. MTS has been dominating in math, logic, and computer science, and therefore is accepted by the majority people. Even so, it has been attacked by other people (not only the EGS believers) for many reasons. A while ago I made a figure to illustrate this difference, which is at http://nars.wang.googlepages.com/wang.semantics-figure.pdf . A manifesto of EGS is at http://nars.wang.googlepages.com/wang.semantics.pdf Since the debate on the nature of truth and meaning has existed for thousands of years, I don't think we can settle down it here by some email exchanges. I just want to let the interested people know the theoretical background of the related discussions. Pei On Sat, Oct 11, 2008 at 8:34 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly the difference between an experience-grounded semantics and a model-theoretic semantics. I don't agree with this distinction ... unless you are construing model theoretic semantics in a very restrictive way, which then does not apply to PLN. If by model-theoretic semantics you mean something like what Wikipedia says at http://en.wikipedia.org/wiki/Formal_semantics, *** Model-theoretic semantics is the archetype of Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of model theory. This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively specified group of interpretation functions from them to some predefined mathematical domains: an interpretation of first-order predicate logic is given by a mapping from terms to a universe of individuals, and a mapping from propositions to the truth values true and false. *** then yes, PLN's semantics is based on a mapping from terms to a universe of individuals, and a mapping from propositions to truth values. On the other hand, these individuals may be for instance **elementary sensations or actions**, rather than higher-level individuals like, say, a specific cat, or the concept cat. So there is nothing non-experience-based about mapping terms into a individuals that are the system's direct experience ... and then building up more abstract terms by grouping these directly-experience-based terms. IMO, the dichotomy between experience-based and model-based semantics is a misleading one. Model-based semantics has often been used in a non-experience-based way, but that is not because it fundamentally **has** to be used in that way. To say
Re: [agi] two types of semantics [Was: NARS and probability]
On the other hand, in PLN's indefinite probabilities there is a parameter k which plays a similar mathematical role, yet **is** explicitly interpreted as being about a number of hypothetical future observations ... Clearly the interplay btw algebra and interpretation is one of the things that makes this area of research (uncertain logic) interesting ... ben g On Sun, Oct 12, 2008 at 2:07 PM, Pei Wang [EMAIL PROTECTED] wrote: Abram: The parameter 'k' does not really depend on the future, because it makes no assumption about what will happen in that period of time. It is just a ruler or weight (used with scale) to measure the amount of evidence, as a reference amount. For other people: The definition of confidence c = w/(w+k) states that confidence is the proportion of current evidence among future evidence, after the coming of evidence of amount k. Pei On Sun, Oct 12, 2008 at 1:48 PM, Abram Demski [EMAIL PROTECTED] wrote: Pei, In this context, how do you justify the use of 'k'? It seems like, by introducing 'k', you add a reliance on the truth of the future after k observations into the semantics. Since the induction/abduction formula is dependent on 'k', the truth values that result no longer only summarize experience; they are calculated with prediction in mind. --Abram On Sun, Oct 12, 2008 at 8:29 AM, Pei Wang [EMAIL PROTECTED] wrote: A brief and non-technical description of the two types of semantics mentioned in the previous discussions: (1) Model-Theoretic Semantics (MTS) (1.1) There is a world existing independently outside the intelligent system (human or machine). (1.2) In principle, there is an objective description of the world, in terms of objects, their properties, and relations among them. (1.3) Within the intelligent system, its knowledge is an approximation of the objective description of the world. (1.4) The meaning of a symbol within the system is the object it refers to in the world. (1.5) The truth-value of a statement within the system measures how close it approximates the fact in the world. (2) Experience-Grounded Semantics (EGS) (2.1) There is a world existing independently outside the intelligent system (human or machine). [same as (1.1), but the agreement stops here] (2.2) Even in principle, there is no objective description of the world. What the system has is its experience, the history of its interaction of the world. (2.3) Within the intelligent system, its knowledge is a summary of its experience. (2.4) The meaning of a symbol within the system is determined by its role in the experience. (2.5) The truth-value of a statement within the system measures how close it summarizes the relevant part of the experience. To further simplify the description, in the context of learning and reasoning: MTS takes objective truth of statements and real meaning of terms as aim of approximation, while EGS refuses them, but takes experience (input data) as the only thing to depend on. As usual, each theory has its strength and limitation. The issue is which one is more proper for AGI. MTS has been dominating in math, logic, and computer science, and therefore is accepted by the majority people. Even so, it has been attacked by other people (not only the EGS believers) for many reasons. A while ago I made a figure to illustrate this difference, which is at http://nars.wang.googlepages.com/wang.semantics-figure.pdf . A manifesto of EGS is at http://nars.wang.googlepages.com/wang.semantics.pdf Since the debate on the nature of truth and meaning has existed for thousands of years, I don't think we can settle down it here by some email exchanges. I just want to let the interested people know the theoretical background of the related discussions. Pei On Sat, Oct 11, 2008 at 8:34 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly the difference between an experience-grounded semantics and a model-theoretic semantics. I don't agree with this distinction ... unless you are construing model theoretic semantics in a very restrictive way, which then does not apply to PLN. If by model-theoretic semantics you mean something like what Wikipedia says at http://en.wikipedia.org/wiki/Formal_semantics, *** Model-theoretic semantics is the archetype of Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of model theory. This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively
Re: [agi] two types of semantics [Was: NARS and probability]
True. Similar parameters can be found in the work of Carnap and Walley, with different interpretations. Pei On Sun, Oct 12, 2008 at 2:11 PM, Ben Goertzel [EMAIL PROTECTED] wrote: On the other hand, in PLN's indefinite probabilities there is a parameter k which plays a similar mathematical role, yet **is** explicitly interpreted as being about a number of hypothetical future observations ... Clearly the interplay btw algebra and interpretation is one of the things that makes this area of research (uncertain logic) interesting ... ben g On Sun, Oct 12, 2008 at 2:07 PM, Pei Wang [EMAIL PROTECTED] wrote: Abram: The parameter 'k' does not really depend on the future, because it makes no assumption about what will happen in that period of time. It is just a ruler or weight (used with scale) to measure the amount of evidence, as a reference amount. For other people: The definition of confidence c = w/(w+k) states that confidence is the proportion of current evidence among future evidence, after the coming of evidence of amount k. Pei On Sun, Oct 12, 2008 at 1:48 PM, Abram Demski [EMAIL PROTECTED] wrote: Pei, In this context, how do you justify the use of 'k'? It seems like, by introducing 'k', you add a reliance on the truth of the future after k observations into the semantics. Since the induction/abduction formula is dependent on 'k', the truth values that result no longer only summarize experience; they are calculated with prediction in mind. --Abram On Sun, Oct 12, 2008 at 8:29 AM, Pei Wang [EMAIL PROTECTED] wrote: A brief and non-technical description of the two types of semantics mentioned in the previous discussions: (1) Model-Theoretic Semantics (MTS) (1.1) There is a world existing independently outside the intelligent system (human or machine). (1.2) In principle, there is an objective description of the world, in terms of objects, their properties, and relations among them. (1.3) Within the intelligent system, its knowledge is an approximation of the objective description of the world. (1.4) The meaning of a symbol within the system is the object it refers to in the world. (1.5) The truth-value of a statement within the system measures how close it approximates the fact in the world. (2) Experience-Grounded Semantics (EGS) (2.1) There is a world existing independently outside the intelligent system (human or machine). [same as (1.1), but the agreement stops here] (2.2) Even in principle, there is no objective description of the world. What the system has is its experience, the history of its interaction of the world. (2.3) Within the intelligent system, its knowledge is a summary of its experience. (2.4) The meaning of a symbol within the system is determined by its role in the experience. (2.5) The truth-value of a statement within the system measures how close it summarizes the relevant part of the experience. To further simplify the description, in the context of learning and reasoning: MTS takes objective truth of statements and real meaning of terms as aim of approximation, while EGS refuses them, but takes experience (input data) as the only thing to depend on. As usual, each theory has its strength and limitation. The issue is which one is more proper for AGI. MTS has been dominating in math, logic, and computer science, and therefore is accepted by the majority people. Even so, it has been attacked by other people (not only the EGS believers) for many reasons. A while ago I made a figure to illustrate this difference, which is at http://nars.wang.googlepages.com/wang.semantics-figure.pdf . A manifesto of EGS is at http://nars.wang.googlepages.com/wang.semantics.pdf Since the debate on the nature of truth and meaning has existed for thousands of years, I don't think we can settle down it here by some email exchanges. I just want to let the interested people know the theoretical background of the related discussions. Pei On Sat, Oct 11, 2008 at 8:34 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly the difference between an experience-grounded semantics and a model-theoretic semantics. I don't agree with this distinction ... unless you are construing model theoretic semantics in a very restrictive way, which then does not apply to PLN. If by model-theoretic semantics you mean something like what Wikipedia says at http://en.wikipedia.org/wiki/Formal_semantics, *** Model-theoretic semantics is the archetype of Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of
Re: [agi] two types of semantics [Was: NARS and probability]
Pei, You are right, it doesn't make any such assumptions while Bayesian practice does. But, the parameter 'k' still fixes the length of time into the future that we are interested in predicting, right? So it seems to me that the truth value must be predictive, if its calculation depends on what we want to predict. That is why 'k' is hard to incorporate into the probabilistic NARSian scheme I want to formulate... --Abram On Sun, Oct 12, 2008 at 2:07 PM, Pei Wang [EMAIL PROTECTED] wrote: Abram: The parameter 'k' does not really depend on the future, because it makes no assumption about what will happen in that period of time. It is just a ruler or weight (used with scale) to measure the amount of evidence, as a reference amount. For other people: The definition of confidence c = w/(w+k) states that confidence is the proportion of current evidence among future evidence, after the coming of evidence of amount k. Pei On Sun, Oct 12, 2008 at 1:48 PM, Abram Demski [EMAIL PROTECTED] wrote: Pei, In this context, how do you justify the use of 'k'? It seems like, by introducing 'k', you add a reliance on the truth of the future after k observations into the semantics. Since the induction/abduction formula is dependent on 'k', the truth values that result no longer only summarize experience; they are calculated with prediction in mind. --Abram On Sun, Oct 12, 2008 at 8:29 AM, Pei Wang [EMAIL PROTECTED] wrote: A brief and non-technical description of the two types of semantics mentioned in the previous discussions: (1) Model-Theoretic Semantics (MTS) (1.1) There is a world existing independently outside the intelligent system (human or machine). (1.2) In principle, there is an objective description of the world, in terms of objects, their properties, and relations among them. (1.3) Within the intelligent system, its knowledge is an approximation of the objective description of the world. (1.4) The meaning of a symbol within the system is the object it refers to in the world. (1.5) The truth-value of a statement within the system measures how close it approximates the fact in the world. (2) Experience-Grounded Semantics (EGS) (2.1) There is a world existing independently outside the intelligent system (human or machine). [same as (1.1), but the agreement stops here] (2.2) Even in principle, there is no objective description of the world. What the system has is its experience, the history of its interaction of the world. (2.3) Within the intelligent system, its knowledge is a summary of its experience. (2.4) The meaning of a symbol within the system is determined by its role in the experience. (2.5) The truth-value of a statement within the system measures how close it summarizes the relevant part of the experience. To further simplify the description, in the context of learning and reasoning: MTS takes objective truth of statements and real meaning of terms as aim of approximation, while EGS refuses them, but takes experience (input data) as the only thing to depend on. As usual, each theory has its strength and limitation. The issue is which one is more proper for AGI. MTS has been dominating in math, logic, and computer science, and therefore is accepted by the majority people. Even so, it has been attacked by other people (not only the EGS believers) for many reasons. A while ago I made a figure to illustrate this difference, which is at http://nars.wang.googlepages.com/wang.semantics-figure.pdf . A manifesto of EGS is at http://nars.wang.googlepages.com/wang.semantics.pdf Since the debate on the nature of truth and meaning has existed for thousands of years, I don't think we can settle down it here by some email exchanges. I just want to let the interested people know the theoretical background of the related discussions. Pei On Sat, Oct 11, 2008 at 8:34 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly the difference between an experience-grounded semantics and a model-theoretic semantics. I don't agree with this distinction ... unless you are construing model theoretic semantics in a very restrictive way, which then does not apply to PLN. If by model-theoretic semantics you mean something like what Wikipedia says at http://en.wikipedia.org/wiki/Formal_semantics, *** Model-theoretic semantics is the archetype of Alfred Tarski's semantic theory of truth, based on his T-schema, and is one of the founding concepts of model theory. This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively specified group of interpretation functions from them to
Re: [agi] two types of semantics [Was: NARS and probability]
On Sun, Oct 12, 2008 at 3:06 PM, Abram Demski [EMAIL PROTECTED] wrote: Pei, You are right, it doesn't make any such assumptions while Bayesian practice does. But, the parameter 'k' still fixes the length of time into the future that we are interested in predicting, right? So it seems to me that the truth value must be predictive, if its calculation depends on what we want to predict. The truth-value is defined/measured according to past experience, but is used to predict future experience. Especially, this is what the expectation function is about. But still, a high expectation only means that the system will behave under the assumption that the statement may be confirmed again, which by no means guarantee the actual confirmation of the statement in the future. That is why 'k' is hard to incorporate into the probabilistic NARSian scheme I want to formulate... For this purpose, the interval version of the truth value may be easier. Pei --Abram On Sun, Oct 12, 2008 at 2:07 PM, Pei Wang [EMAIL PROTECTED] wrote: Abram: The parameter 'k' does not really depend on the future, because it makes no assumption about what will happen in that period of time. It is just a ruler or weight (used with scale) to measure the amount of evidence, as a reference amount. For other people: The definition of confidence c = w/(w+k) states that confidence is the proportion of current evidence among future evidence, after the coming of evidence of amount k. Pei On Sun, Oct 12, 2008 at 1:48 PM, Abram Demski [EMAIL PROTECTED] wrote: Pei, In this context, how do you justify the use of 'k'? It seems like, by introducing 'k', you add a reliance on the truth of the future after k observations into the semantics. Since the induction/abduction formula is dependent on 'k', the truth values that result no longer only summarize experience; they are calculated with prediction in mind. --Abram On Sun, Oct 12, 2008 at 8:29 AM, Pei Wang [EMAIL PROTECTED] wrote: A brief and non-technical description of the two types of semantics mentioned in the previous discussions: (1) Model-Theoretic Semantics (MTS) (1.1) There is a world existing independently outside the intelligent system (human or machine). (1.2) In principle, there is an objective description of the world, in terms of objects, their properties, and relations among them. (1.3) Within the intelligent system, its knowledge is an approximation of the objective description of the world. (1.4) The meaning of a symbol within the system is the object it refers to in the world. (1.5) The truth-value of a statement within the system measures how close it approximates the fact in the world. (2) Experience-Grounded Semantics (EGS) (2.1) There is a world existing independently outside the intelligent system (human or machine). [same as (1.1), but the agreement stops here] (2.2) Even in principle, there is no objective description of the world. What the system has is its experience, the history of its interaction of the world. (2.3) Within the intelligent system, its knowledge is a summary of its experience. (2.4) The meaning of a symbol within the system is determined by its role in the experience. (2.5) The truth-value of a statement within the system measures how close it summarizes the relevant part of the experience. To further simplify the description, in the context of learning and reasoning: MTS takes objective truth of statements and real meaning of terms as aim of approximation, while EGS refuses them, but takes experience (input data) as the only thing to depend on. As usual, each theory has its strength and limitation. The issue is which one is more proper for AGI. MTS has been dominating in math, logic, and computer science, and therefore is accepted by the majority people. Even so, it has been attacked by other people (not only the EGS believers) for many reasons. A while ago I made a figure to illustrate this difference, which is at http://nars.wang.googlepages.com/wang.semantics-figure.pdf . A manifesto of EGS is at http://nars.wang.googlepages.com/wang.semantics.pdf Since the debate on the nature of truth and meaning has existed for thousands of years, I don't think we can settle down it here by some email exchanges. I just want to let the interested people know the theoretical background of the related discussions. Pei On Sat, Oct 11, 2008 at 8:34 PM, Ben Goertzel [EMAIL PROTECTED] wrote: Hi, What this highlights for me is the idea that NARS truth values attempt to reflect the evidence so far, while probabilities attempt to reflect the world I agree that probabilities attempt to reflect the world . Well said. This is exactly the difference between an experience-grounded semantics and a model-theoretic semantics. I don't agree with this distinction ... unless you are construing model theoretic semantics in a very restrictive way, which then does not apply to
