- From: Pat Hayes <phayes@ai.uwf.edu>
- Date: Fri, 12 Oct 2001 12:38:48 -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 these rules and the corresponding implications. >> >> Why not? The 2-valued status of the logic says nothing about how to >> interpret *rules*. > >Notice that we can associate a model-theoretic semantics with rules >in a natural way: an interpretation I satisfies a rule (is a model >of it) if it satisfies its consequent whenever it satisfies its >antecedcent. With this interpretation, the rule has exactly the same meaning as the implication, indeed. So there would seem to be little utility in making the distinction between rules and implications. However, that is not the way that the KIF authors are intending to use the term 'rule'; they would describe that as the KIF *sentence* (implies <antecedent> <consequent>). > > >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. > >Yes, we can infer from a rule set: using the above definition of a >model of a rule, we can define that a rule set R entails a sentence F >if all models of R satisfy F (in logic programming we say that >R entails F if all stable models of R satisfy F). > >> >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. > >I think you confuse something here: Triggering a rule is a different >(proof-procedural) thing than the model-theoretic semantics of rules. I am vividly aware of the distinction. It is precisely the point I am trying to get across to you. Rules, in the sense used by the KIF authors, *are* a proof-procedural matter: that is why they are called 'rules' rather than, say, 'implications', you see, and why a notational convention has been introduced into the syntax to state them differently. >Again: Let M be a classical model of the two rules (that is, it >satisfies their consequent if it satisfies their antecequent). Then >either M satisfies (citizen Joe), in which case it has to satisfy >(status-known Joe) because it satisfies the first rule, or it satisfies >(not (citizen Joe)), in which case it has to satisfy (status-known Joe) >because it also satisfies the second rule. Yes, you have already made that point. But the fact that M is either true or false is not sufficient, of itself, to permit one to either assert M or to assert (not M). A rule is invoked only by an assertion. Neither of these rules has a disjunction as an antecedent, so your argument is irrelevant. You are confusing rules with material implications. >So, the author of this text on KIF seems to make a mistake here. I wish you would not keep accusing other people of making mistakes because they are not using your particular conventions. The KIF author(s) were not making a 'mistake'; they were pointing out that rules can be understood differently from implications. You seem to be unable to appreciate their point, insist on interpreting rules as implications, find that their example does not make their point *under this assumption*, the very assumption they are rejecting, and then accuse them of making a mistake. The mistake is yours, my dear fellow. 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 Friday, 12 October 2001 13:38:54 UTC