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Re: Review of FLD

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>
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
> 


-- 
    -- michael
Received on Tuesday, 19 May 2009 15:33:03 GMT

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