- From: Pat Hayes <phayes@ai.uwf.edu>
- Date: Thu, 11 Oct 2001 18:24:59 -0500
- To: "Wagner, G.R." <G.R.Wagner@tm.tue.nl>
- Cc: www-rdf-rules@w3.org
> > I always liked the example that was given in the KIF documentation >> (KIF 3.0 Ref. Manual, >> http://logic.stanford.edu/kif/Hypertext/node37.html): >> >> ... On the other hand, in some cases, replacing <<= by <= would be >> semantically unacceptable. For instance, the rules >> >> (<<= (status-known ?x) (citizen ?x)) >> (<<= (status-known ?x) (not (citizen ?x))) >> >> allow us to infer (status-known Joe) only if one of the sentences >> >> (citizen Joe), (not (citizen Joe)) >> >> can be inferred. Replacing the rules by implications would make >> (status-known ?x) identically true." > >But according to classical (2-valued) logic, there is no difference >here between the rules and the corresponding implications. Why not? The 2-valued status of the logic says nothing about how to interpret *rules*. That is the point being made by the KIF authors: one is not obliged to consider a rule as meaning the same as an implication. An implication is an assertion in the language; an rule is a licence to perform an inference. The deduction theorem in classical logic shows that they are closely connected, in that the implication (implies A B) is valid (true in all models) just when the rule (from A infer B) is also valid (ie when A entails B); but this is simply a fact about the semantic relationship between an expression and a rule. It does not create any kind of imperative that any deductive processor must obey every rule, particularly if the corresponding implication is not valid. Sometimes, one can utilize a restriction on a rule to convey the presence of more information than could be inferred using the implication alone, as is obviously intended in this case by the use of 'status-known', which seems to convey the meaning of something being provable rather than simply true. KIF is richly endowed with meta-descriptive abilities which make such usages quite natural to contemplate. >The >sentence (status-known Joe) could also be inferred from the >two rules alone, From the two implications, but not from the rules. In fact, strictly speaking, nothing can be inferred *from* a rule, only *by* a rule. >since every classical (i.e. total and coherent) >model of the two rules would satisfy it, simply because it would >either satisfy (citizen Joe) or (not (citizen Joe)), and in both >cases, as it satisfies both rules, it would also have to satisfy >(status-known Joe). (I think you mean, as it satisfies *one of the* rules?). But merely being satisfiable in a single interpretation is not sufficient to trigger a rule. >So, the author of this text on KIF seems to make a mistake here. >In fact, he unintentionally describes the behavior of rules in >extended logic programs where "not" corresponds to the strong >(monotonic) negation of partial logic, where models are partial >and the "tertium non datur" (= law of the excluded middle) does >not hold. No, that is not correct. For some reason, you are denying the obvious point being made here, and then going on to draw inappropriate conclusions from your misapprehension. The very point being made is that a rule need not be understood as an implication, so there is no need to deny the tertium. Pat Hayes -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes
Received on Thursday, 11 October 2001 19:25:07 UTC