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 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/?&; >> > 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/?&; >> Powered by Listbox: http://www.listbox.com > > > > -- > Ben Goertzel, PhD > CEO, Novamente LLC and Biomind LLC > Director of Research, SIAI > [EMAIL PROTECTED] > > "Nothing will ever be attempted if all possible objections must be first > overcome " - Dr Samuel Johnson > > > ________________________________ > 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/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
