From: Ian Horrocks (horrocks@cs.man.ac.uk)
Date: 01/30/01
Peter, This was basically my first idea, but Uli Sattler pointed out that there are serious problems with the negation of modal atoms. Let's say we have x R d, x abstract and d concrete, and x has no other R successors. x is not in the restriction hasType R C for some abstract class C, so it is in the negation of that restriction. That means that it is in the restriction toType R (not C). The semantics of this restriction say that every R successor is a (not C). The semantics you want for negation makes (not C) be a subset of the abstract domain, but we have an R successor d that is in the concrete domain. Ian On January 30, Peter F. Patel-Schneider writes: > This problem can be removed by employing the (admittedly counter-intuitive) > notion of having complement be relative to the abstract sub-domain. > > peter > > > From: Ian Horrocks <horrocks@cs.man.ac.uk> > Subject: Re: Suggested changes to concrete datatypes proposal > Date: Tue, 30 Jan 2001 18:38:20 +0000 (GMT) > > > Peter, > > > > As you say, preventing 3 from degenerating into 1 is difficult. I > > think that what you have proposed below suffers from the problem I > > mentioned in my reply to Jeff. i.e., when you negate modal atoms you > > get an implicit union of abstract and concrete types. This is the > > reason for having separate concrete and abstract properties. > > > > Ian
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