--- On Fri, 9/19/08, Jan Klauck <[EMAIL PROTECTED]> wrote: > Formal logic doesn't scale up very well in humans. That's why this > kind of reasoning is so unpopular. Our capacities are that > small and we connect to other human entities for a kind of > distributed problem solving. Logic is just a tool for us to > communicate and reason systematically about problems we would > mess up otherwise.
Exactly. That is why I am critical of probabilistic or uncertain logic. Humans are not very good at logic and arithmetic problems requiring long sequences of steps, but duplicating these defects in machines does not help. It does not solve the problem of translating natural language into formal language and back. When we need to solve such a problem, we use pencil and paper, or a calculator, or we write a program. The problem for AI is to convert natural language to formal language or a program and back. The formal reasoning we already know how to do. Even though a language model is probabilistic, probabilistic logic is not a good fit. For example, in NARS we have deduction (P->Q, Q->R) => (P->R), induction (P->Q, P->R) => (Q->R), and abduction (P->R, Q->R) => (P->Q). Induction and abduction are not strictly true, of course, but in a probabilistic logic we can assign them partial truth values. For language modeling, we can simplify the logic. If we accept the "converse" rule (P->Q) => (Q->P) as partially true (if rain predicts clouds, then clouds may predict rain), then we can derive induction and abduction from deduction and converse. For induction, (P->Q, P->R) => (Q->P, P->R) => (Q->R). Abduction is similar. Allowing converse, the statement (P->Q) is really a fuzzy equivalence or association (P ~ Q), e.g. (rain ~ clouds). A language model is a set of associations between concepts. Language learning consists of two operations carried out on a massively parallel scale: forming associations and forming new concepts by clustering in context space. An example of the latter is: the dog is the cat is the house is ... the (noun) is So if we read "the glorp is" we learn that "glorp" is a noun. Likewise, we learn something of its meaning from its more distant context, e.g. "the glorp is eating my flowers". We do this by the transitive property of association, e.g. (glorp ~ eating flowers ~ rabbit). This is not to say NARS or other systems are wrong, but rather that they have more capability than we need to solve reasoning in AI. Whether the extra capability helps or not is something that requires experimental verification. -- Matt Mahoney, [EMAIL PROTECTED] ------------------------------------------- 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=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
