- From: Drew McDermott <drew.mcdermott@yale.edu>
- Date: Fri, 1 Jul 2005 22:39:29 -0400
- To: www-rdf-rules@w3.org
> > [me]
> > I am somewhat baffled. If two systems use the same syntax, and employ
> > the same vocabulary with the same (Tarskian) semantics ... [then
> > they can interoperate by exchanging messages]
> [Ian Horrocks]
> [...]
> They use the same model structure, but LP semantics admits many fewer
> models than FO semantics, and fewer models means more entailments.
But entailments just _cannot_ be part of the meaning of a set of
assertions. If that were the case, then a nonmonotonic system
couldn't interoperate with itself!
Suppose Cn(X,Y) is a nonmonotonic consequence relation, giving the
entailments from X when combined with the disjoint set Y. (Cn can be
defined using stable models, well-founded models, or whatever.)
If we focus just on the entailments of X itself, we can define E(X,Y)
to be Cn(X,Y)\Cn(Y,{}), the statements entailed by X over and above
the statements entailed by Y. But then E(X,Y) can differ from E(X,Z)
in many cases. Must we say that X means something different when
conjoined with Y than what it means when conjoined with Z? Two
nonmonotonic systems can interoperate, according to this view, only if
they happen to have reached the same conclusions. This seems to be a
reductio ad absurdum of the whole idea.
The whole "minimal model," "stable model," etc. family of mechanisms
are devices for specifying precisely --- and hopefully efficiently ---
what follows from a set of premises. But the use of the word "model"
all over this landscape doesn't mean we're talking about the
_semantics_ of the statements involved. A theorem of the form
The entailments from statements S
= the set of statements true in
all models of S with property P
should not be read as if it were changing the set of models of S.
-- Drew
--
-- Drew McDermott
Yale University
Computer Science Department
Received on Saturday, 2 July 2005 02:38:27 UTC