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Re: revised version of semantics document

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 20 Aug 2002 07:00:19 -0400
To: phayes@ai.uwf.edu
Cc: www-webont-wg@w3.org
Message-Id: <20020820070019A.pfps@research.bell-labs.com>

From: pat hayes <phayes@ai.uwf.edu>
Subject: revised version of semantics document
Date: Tue, 20 Aug 2002 03:06:03 -0700

> I only just read Peter's comments, but I do not follow them. Both of 
> the entailments that he says are not present:
> E1/ John in Student intersect Employee
> 	    entails
> 	    John in Employee intersect Student
>     	E2/ John in atleast 2 friend
> 	    entails
> 	    John in atleast 1 friend
> are in fact supported by the MT in the document, seems to me. Since 
> the basic semantic conditions are transcribed from his OWL MT this 
> should not be hard to see. If Im  missing something, please tell me 
> what.

Consider E1 in more detail.  Its premise is

	John rdf:type _:x .
	_:x owl:intersectionOf _:l1 .
	_:l1 owl:first Student .
	_:l1 owl:rest _:l2 .
	_:l2 owl:first Employee .
	_:l2 owl:rest owl:nil.

and its conclusion is

	John rdf:type _:y .
	_:y owl:intersectionOf _:l3 .
	_:l3 owl:first Student .
	_:l3 owl:rest _:l4 .
	_:l4 owl:first Employee .
	_:l4 owl:rest owl:nil.

An interpretation of the premise above does not require the presence of the
list in the conclusion.

A GHOWL interpretation of the premise (ignoring some built-in stuff) is

	IR = { j, t, x, i, l1, l2, s, e, f, r, n }

	IS(John) = j
	IS(rdf:type) = t
	IS(owl:intersectionOf) = i
	IS(Student) = s
	IS(Employee) = e
	IS(owl:first) = f
	IS(owl:rest) = r
	IS(owl:nil) = n

	ICEXT(s) = { j }
	ICEXT(e) = { j }
	ICEXT(x) = { j }
	
	IEXT(j) = { }
	IEXT(t) = [see above]
	IEXT(x) = { } 
	IEXT(i) = { <x,l1> }
	IEXT(l1) = { }
	IEXT(l2) = { }
	IEXT(s) = { }
	IEXT(f) = { }
	IEXT(f) = { <l1,s>, <l2,e> }
	IEXT(r) = { <l1,l2>, <l2,n> }
	IEXT(n) = { }

This is not a GHOWL interpretation of the conclusion because there is no
domain element related via I(owl:first) to I(Employee) and related via
I(owl:rest) to I(owl:nil).  QED


My semantics has interpretations that are extensions of RDFS
interpretations, but the abstract syntax on which my semantics works is not
RDF graphs.  Therefore there are no triples, and thus no RDFS
semantic conditions on triples to block this kind of entailment.  To make
these sorts of entailments go through when using RDF graphs requires
darkening a lot of triples.


Peter F. Patel-Schneider
Bell Labs Research
Received on Tuesday, 20 August 2002 07:00:28 GMT

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