RE: Expressiveness of RDF as Rule Conclusion Language (was Re: W hat is an RDF Query? )

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Fri, 12 Oct 2001 12:38:48 -0500
Message-Id: <p05101005b7ecd38ca670@[205.160.76.193]>
To: "Wagner, G.R." <G.R.Wagner@tm.tue.nl>

```>  > >  > 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
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Received on Friday, 12 October 2001 13:38:54 GMT

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