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Propositional Circumscriptions

Yves Moinard 1 Raymond Rolland 2
1 REPCO - Knowledge Representation
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : Circumscription formalizes in terms of classical logic various aspects of common sense reasoning: exceptions are made as rare as possible from the given knowledge. We give the main properties of the reasoning thanks to circumscriptions. We provide various counter-examples to prove some counter-properties. We restrict our study to propositional circumscriptions, and we show that even in this case, things are not that easy. We evoke the predicate calculus case, showing that the propositional case suffices to get a good understanding of the logical properties of circumscriptions in any case. As we stick to traditional circumscriptions, we have adapted significantly the literature on «preferential models». We study carefully the more general «formula circumscription», examining when sets of formulas give rise to the same circumscription, and providing the first known characterization result. Finally, an intuitive presentation of some of these (counter-) properties is given. Examples of real circumscriptions illustrate the utility of this study for translating a common sense situation in terms of circumscription. This part contains arguments against some classical methods and proposes new methods instead, which have a better behavior and use simpler circumscriptions than the classical methods. Our study can be considered as giving the first steps towards an automatic way of translating sets of rules in terms of circumscription, which should allow to use seriously circumscription for what it has been proposed till the beginning. Also, as we describe syntactically all the sets of formulas which give rise to some given propositional circumscription, this study should help the automatization.
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https://hal.inria.fr/inria-00073147
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 11:59:11 AM
Last modification on : Thursday, February 11, 2021 - 2:48:04 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:35:42 PM

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  • HAL Id : inria-00073147, version 1

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Yves Moinard, Raymond Rolland. Propositional Circumscriptions. [Research Report] RR-3538, INRIA. 1998. ⟨inria-00073147⟩

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