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NAF and NEG [was: LP Semantics (non-monotonicity) in Usage Scenarios?]

From: Gerd Wagner <wagnerg@tu-cottbus.de>
Date: Mon, 29 Aug 2005 11:00:29 +0200
To: "'Michael Kifer'" <kifer@cs.sunysb.edu>
Cc: <public-rule-workshop-discuss@w3.org>, <analyti@ics.forth.gr>, 'Carlos Viegas Damasio' <cd@di.fct.unl.pt>, <antoniou@ics.forth.gr>
Message-Id: <20050829090157.6C67F50821E@smtp2.TU-Cottbus.De>

> By the way, we are not advocating for NAF at the exclusion of 
> classical negation. There are extensions of LP, which support 
> classical negation as well (flora-2 doesn't support that yet). 

That's not quite true, Michael: the second negation (e.g. in 
extended logic programs as defined by Gelfond and Lifschitz) is 
only called "classical", but it is not clasical negation because
it does not obey the law of the excluded middle (LEM). And this 
should not come as a surprise: the LEM creates a certain kind of 
indefiniteness (e.g. it implies the principle of reasoning by 
cases) that cannot be handled by a computational system without
severe restrictions (such as DL).

Therefore the second negation in these formalisms does not 
correspond to classical 2-valued (i.e. Boolean) negation, but 
rather to 3/4-valued Kleene negation.

These 2 negations are also available in RuleML. Notice 
also that there is an ISWC'05 paper about extending RDF by 
adding these 2 negations (NAF and Kleene-NEG) to it [1].

-Gerd

[1] A. Analyti, G. Antoniou1, C. V. Damasio and G. Wagner:
Stable Model Theory for Extended RDF Ontologies
http://www.informatik.tu-cottbus.de/~gwagner/REWERSE-I1/ERDF-ISWC-05.pdf


--------------------------------------------
Professor Gerd Wagner 
http://www.informatik.tu-cottbus.de/~gwagner
Email: G.Wagner@tu-cottbus.de
Tel: (+49 355) 69 2397
Institute of Informatics
Brandenburg University of Technology 
at Cottbus, Germany
Received on Monday, 29 August 2005 09:02:08 GMT

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