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Re: Review of FLD

From: Chris Welty <cawelty@gmail.com>
Date: Tue, 19 May 2009 08:30:58 -0400
Message-ID: <4A12A682.20801@gmail.com>
To: kifer@cs.sunysb.edu
CC: "Public-Rif-Wg (E-mail)" <public-rif-wg@w3.org>


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.


Dr. Christopher A. Welty                    IBM Watson Research Center
+1.914.784.7055                             19 Skyline Dr.
cawelty@gmail.com                           Hawthorne, NY 10532
Received on Tuesday, 19 May 2009 12:31:44 UTC

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