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: 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
