- From: Drew McDermott <drew.mcdermott@yale.edu>
- Date: Fri, 12 Oct 2001 09:29:57 -0400 (EDT)
- To: www-rdf-rules@w3.org
[Gerd Wagner]
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.
> >The sentence (status-known Joe) could also be inferred from the
> >two rules alone,
>
[Pat Hayes]
> 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).
You're assuming that a what a rule set entails by your definition is
equivalent to what is inferrable. That is, you're assuming that the
theory + rules is complete. But the sort of rule in question here
gives rise to incompleteness for precisely the reasons you describe:
'(status-known Joe)' is true in all models, but can't be inferred.
This may be an argument against your proposed model-theoretic
semantics for rules.
-- Drew McDermott
Received on Friday, 12 October 2001 09:30:00 UTC