- From: Enrico Franconi <franconi@inf.unibz.it>
- Date: Wed, 11 Dec 2002 19:04:03 +0000
- To: "Wagner, G.R." <G.R.Wagner@tm.tue.nl>
- Cc: "'pat hayes'" <phayes@ai.uwf.edu>, Sandro Hawke <sandro@w3.org>, www-rdf-rules@w3.org, timbl@w3.org, pfps@research.bell-labs.com
On December 11, Wagner, G.R. writes:
> > (or, possibly, that you are using it relative to a more
> > 'computational' semantics, such as minimal-model semantics,
> > relative to which it is complete; but then you ought to think hard
> > about whether you still want to call it the material conditional,
> > maybe.)
>
> Under the minimal model semantics, a rule does no longer have the
> same intended models as the corresponding implication. This is easy
> to see: consider the rule q :- ~p. It has only one intended (i.e.
> minimal) model, which may be expressed by the set {q}, whereas the
> corresponding material implication ~p -> q, which is equivalent to q
> v p, has two intended/minimal models: {q} and {p}.
I suspect that this is the origin of the misunderstanding underlying
this discussion. To me, rules in knowledge representation ALWAYS have
a minimal model semantics or something similar. In fact, they are
meant to be applied to a specific unique non-ambiguous situation of
the world (e.g., the EDB in datalog, or a DB in SQL views, or the fact
base in Prolog, etc). This is what makes them rules in knowledge
representation as opposed to material implications. A formulas with a
material implication is not a rule since its semantics is classical
FOL semantics, i.e., it is understood wrt all the interpretations
satisfying it and not only wrt the minimal (or preferred) one.
cheers
-- e.
Enrico Franconi - franconi@inf.unibz.it
Free University of Bozen-Bolzano - http://www.inf.unibz.it/~franconi/
Faculty of Computer Science - Phone: (+39) 0471-315-642
I-39100 Bozen-Bolzano BZ, Italy - Fax: (+39) 0471-315-649
Received on Wednesday, 11 December 2002 13:58:01 UTC