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 that PLN tries to model the world, is then just to say that it tries >> to make probabilistic predictions about sensations and actions that have not >> yet been experienced ... which is certainly the case. >> >>> >>> Once >>> again, the difference in truth-value functions is reduced to the >>> difference in semantics, what is, what the "truth-value" attempts to >>> measure. >> >> Agreed... >> >> Ben G >> >> ________________________________ >> agi | Archives | Modify Your Subscription > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
