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 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 > ------------------------------------------- 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
