- From: Jerome Euzenat <Jerome.Euzenat@inrialpes.fr>
- Date: Thu, 14 Nov 2002 18:01:22 +0100
- To: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>, <www-rdf-logic@w3.org>
Hello,
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
Rewr.
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)
etc.
No, do not ask me for circumscription.
--
Jérôme Euzenat __
/ /\
INRIA Rhône-Alpes, _/ _ _ _ _ _
/_) | ` / ) | \ \ /_)
655, avenue de l'Europe, (___/___(_/_/ / /_(_________________
Montbonnot St Martin, / http://www.inrialpes.fr/exmo
38334 Saint-Ismier cedex, / Jerome.Euzenat@inrialpes.fr
France____________________/ Jerome.Euzenat@free.fr
Received on Thursday, 14 November 2002 12:12:37 UTC