- From: Chris Welty <cawelty@gmail.com>
- Date: Tue, 19 May 2009 08:30:58 -0400
- To: kifer@cs.sunysb.edu
- CC: "Public-Rif-Wg (E-mail)" <public-rif-wg@w3.org>
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 -- Dr. Christopher A. Welty IBM Watson Research Center +1.914.784.7055 19 Skyline Dr. cawelty@gmail.com Hawthorne, NY 10532 http://www.research.ibm.com/people/w/welty
Received on Tuesday, 19 May 2009 12:31:44 UTC