Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
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Artificial Intelligence
Conditional logics of normality: a modal approach
Artificial Intelligence
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Journal of the ACM (JACM)
A Note on the Rational Closure of Knowledge Bases with Both Positive and Negative Knowledge
Journal of Logic, Language and Information
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TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
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JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
A nonmonotonic extension of KLM preferential logic P
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Defeasible inheritance-based description logics
Journal of Artificial Intelligence Research
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This paper provides a general semantic framework for nonmonotonic reasoning, based on a minimal models semantics on the top of KLM systems for nonmonotonic reasoning. This general framework can be instantiated in order to provide a semantic reconstruction within modal logic of the notion of rational closure, introduced by Lehmann and Magidor. We give two characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they are allowed to vary. In both cases a knowledge base must be expanded with a suitable set of consistency assumptions, represented by negated conditionals. The correspondence between rational closure and minimal model semantics suggests the possibility of defining variants of rational closure by changing either the underlying modal logic or the comparison relation on models.