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Re: yet another non-entailment

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 27 Aug 2002 05:36:56 -0400 (EDT)
Message-Id: <20020827.053656.45268298.pfps@research.bell-labs.com>
To: jjc@hplb.hpl.hp.com
Cc: www-webont-wg@w3.org

This message brings up an interesting point about entailments.

Why should I, or Jeremy, or the working group, approve of or disapprove of
a particular entailment?

My stance is clear.  I approve of exactly the entailments that follow from
the model theory.  This is not to say, however, that the model theory is
fixed.  Instead, the model theory can be changed so that certain
entailments follow or do not follow.  However, I do not want to pick
and choose entailments and non-entailments without determining what the
effects would be on the model theory.

Jeremy's stance below appears to be that he will disapprove of entailments
on their own.  Using some aspect of each entailment, taken on its own.  I
find this stance unsupportable, for, taken to its extreme, it would end up
with  K entailing L and L entailing M but K not entailing M, destroying one
of the fundamental properties of entailment.


Now on to the particular entailments below.

Consider the following partial interpretation

<j,a> in IEXT(IS(:p))
<j,b> in IEXT(IS(:p))
<j,a> in IEXT(IS(:q))
<j,b> in IEXT(IS(:q))

This is an interpretation in my model theory, in Dan's model theory (plus
cardinalities), and in Pat's model theory, of the premise below, but not of
the conclusion, taking 2 for iii, 2 for jjj, and 2 for kkk.  So in my view,
no matter what model theory is eventually picked, this is not an
entailment.

However, suppose that 

:r rdfs:domain :A .
:q rdfs:domain :B .
:A owl:disjointWith :B .

is added to the premises.

Then the above interpretation is not an interpretation of the premises.  In
fact, this is now an entailment in all three model theories.  So in my
view, this is now a desirable entailment.

peter


From: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>
Subject: Re: yet another non-entailment (was Re: another revision of semantics document)
Date: Tue, 27 Aug 2002 08:43:50 +0200

> I found one two, or rather an infinite set ...
> 
> for any three natural numbers iii, jjj, kkk such that
>    iii+jjj>=kkk
> 
> following Peter's semantics we have:
> 
> 
> :p rdfs:subPropertyOf :r .
> :q rdfs:subPropertyOf :r .
> 
> entails
> 
> _:x rdf:type rdfs:Class .
> _:x owl:intersectionOf [
>    <<:p owl:minCardinality iii>>
>    <<:q owl:minCardinality jjj>>
> ] .
> _:x rdfs:subClassOf
>    <<:r owl:minCardinility kkk>> .
> 
> (using notation from
> http://www.coginst.uwf.edu/users/phayes/RDFS2OWL-C.html
> )

> Since this entailment uses rather more arithmetic than I feel confortable
> with, I prefer it being a non-entailment.

Personally, I don't have any problem with arithmetic, and I don't
understand why you are uncomfortable with it.

> Jeremy
Received on Tuesday, 27 August 2002 05:37:11 GMT

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