From: Michael Kifer <kifer@cs.sunysb.edu>

Date: Tue, 19 May 2009 11:32:22 -0400

To: Chris Welty <cawelty@gmail.com>

Cc: "Public-Rif-Wg (E-mail)" <public-rif-wg@w3.org>

Message-ID: <20090519113222.50e92647@kiferserv>

Date: Tue, 19 May 2009 11:32:22 -0400

To: Chris Welty <cawelty@gmail.com>

Cc: "Public-Rif-Wg (E-mail)" <public-rif-wg@w3.org>

Message-ID: <20090519113222.50e92647@kiferserv>

Chris, VG's semantics applies only to rules. So, Exists(?x) P(?x) is not a valid syntax as an assertion -- only as a query. So, your example is outside of the syntax of VG or even of any logic programming-style rule language. michael On Tue, 19 May 2009 08:30:58 -0400 Chris Welty <cawelty@gmail.com> wrote: > > Converging.... > > Michael Kifer wrote: > >>>> In a <t,u,f> valued dialect, I'm unsure what happens in this case: > >>>> > >>>> Exists(?x) P(?x) > >>>> Exists(?x) P(a) :- P(?x) > >>>> > >>>> If this entails anything other than P(a), then we would have a hidden > >>>> extension. > >>> Did you mean this? > >>> > >>> (*) P(a) :- Exists(?x) P(?x) > >> No, I meant the example I gave, though (*) is equivalent in a first-order system > >> to my second sentence, and the entailment of the two sentences would of course > >> be P(a). > > > > No, they are NOT equivalent. > > Oh, I see. Stupid syntax. I'm used to quantifiers scoping to the right. So > yes, I did mean (*). > > >>> First, let me say that FLD does not define entailment --- dialects do. > >>> This is a MAJOR point. > >> I'm just wondering what the sensible entailment in a well-founded semantics > >> would be for that, and if it is the same as in a first order system. > > > > Are you using the term "well-founded semantics" in a generic sense or in the > > sense of Van Gelder et al? > > I'm not sure what the generic sense is, I'm loosely familiar with VG. Thinking > about it more, I guess my question is, when you have <t,u,f> as truth values, > what is the truth value of > > (1) Exists P(?x) > > when the model knows of only one object. E.g. if I also have > > (2) Q(a) > > Then is P(a) entailed? > > My question I guess is whether Exists means something different with three truth > values, and whether we should consider calling it something different. > > > -Chris > -- -- michaelReceived on Tuesday, 19 May 2009 15:33:03 UTC

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