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Re: Open world assumption reference

From: Jerome Euzenat <Jerome.Euzenat@inrialpes.fr>
Date: Thu, 14 Nov 2002 18:01:22 +0100
Message-Id: <a05111b08b9f982d306de@[]>
To: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>, <www-rdf-logic@w3.org>


In his message (Open world assumption reference) of 13/11/2002,
Jeremy Carroll wrote:
>What would be a standard reference for the terms:
>  open world assumption
>  closed world assumption
>  monotonic reasoning
>  nonmonotonic reasoning

The reference book on the two first one is the Gallaire/Minker (also 
presents Negation as failure and Clark completion). All these papers, 
very legible, have been reproduced in the Morgan-Kaufmann's readings 
in non monotonic reasoning.

A simple definition of the two last ones is:

Def. Monotonic reasoning (here its entailment):

Given a language L,
for all S included in L,
for all S' included in S,
for all d belonging to L,

if S' |= d, then S |= d.

Paraphrase: The consequences grow monotonically with the set of axioms.

Def. Nonmonotonic reasoning: reasoning which is not monotonic

Given a language L,
there exists S included in L,
there exists S' included in S,
there exists d belonging to L,
such that
S' |= d and S |=/= d.

Example (nonmon). bird(Tweety) |= flies(Tweety)
bird(Tweety), ostrich(Tweety) |=/= flies(Tweety)
bird(Tweety), ostrich(Tweety), firstClassPasenger(Tweety) |= flies(Tweety)

No, do not ask me for circumscription.

  Jérôme Euzenat                  __
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Received on Thursday, 14 November 2002 12:12:37 UTC

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