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RE: Reification -> Higher Order Logic question

From: Spork, Murray <murray.spork@sap.com>
Date: Tue, 28 Sep 2004 01:46:22 +0200
Message-ID: <A54EC476B74FD31186340008C791CBD01019F808@ausydx30.syd.sap.corp>
To: Harry Halpin <hhalpin@ibiblio.org>, www-rdf-logic@w3.org

Hi,

It's not necessarily "obvious" - but discussions of this nature were prevelant during the formalisation of OWL (I think it's safe to say that RDFS's weak semantics meant the issue did not become obvious until the stronger semantics of OWL brought it to the fore - others may correct me on this).

If you search w3.org for "liar's paradox" or "russell's paradox" you will find plenty of discussion.

A quick search found this post from Sandro:
http://lists.w3.org/Archives/Public/www-rdf-logic/2002Sep/0013.html

Hth,

Murray

>-----Original Message-----
>From: www-rdf-logic-request@w3.org 
>[mailto:www-rdf-logic-request@w3.org] On Behalf Of Harry Halpin
>Sent: Tuesday,28 September 2004 8:40 AM
>To: www-rdf-logic@w3.org
>Subject: Reification -> Higher Order Logic question 
>
>
>Apologies for introducing myself with what may be another obvious 
>question, but at a recent XML conference I was at the one continual 
>complaint was that "reification" seems to lead to misleading 
>inferences 
>and is generally hard to fit computationally within an implementation.
>
>I thought about the problem briefly, and it appears that this 
>is similar 
>to the classic higher-order problem of logic, i.e. when one makes 
>quantified predicates about predicates one leaves normal 
>predicate logic and enters
>higher-order logic. It appears that while higher-order logics are more 
>expressive, but their properties make them more difficult, i.e. 
>intractable and harder to make statements about, i.e. in  lower-order 
>logic (My FOL->DL question revisited).  
>
>Does anyone have a good logical story for how RDF reification 
>replicates 
>or has similar behavior? It would seem that this would be one method
>to attempt to state useful things about RDF reified statements, even
>if those inferences were not really DL.
>
>Note the RDF Semantics states this problem clearly:  "Since an 
>assertion 
>of a reification of a triple does not implicitly assert the 
>triple itself, this means that there are no 
>entailment relationships which hold between a triple and a 
>reification of 
>it. Thus the reification vocabulary has no effective semantic 
>constraints 
>on it, other than those that apply to an rdf-interpretation.
>
>A reification of a triple does not entail the triple, and is 
>not entailed 
>by it. (The reification only says that the triple token exists 
>and what it 
>is about, not that it is true. The second non-entailment is a 
>consequence 
>of the fact that asserting a triple does not automatically 
>assert that any 
>triple tokens exist in the universe being described by the triple. For 
>example, the triple might be part of an ontology describing 
>animals, which 
>could be satisfied by an interpretation in which the universe 
>contained 
>only animals, and in which a reification of it was therefore false.)"
>
>Ahhh....which I could see could lead to some non-intuitive reasoning
>and difficulties with implementation. The named graph approach attempts
>to solve this issue, correct?
>
>				--harry
>
>	Harry Halpin
>	Informatics, University of Edinburgh 	
>        http://www.ibiblio.org/hhalpin
>
>
Received on Monday, 27 September 2004 23:46:58 GMT

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