Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
What does a conditional knowledge base entail?
Artificial Intelligence
Conditional logics of normality: a modal approach
Artificial Intelligence
Preferential logics: the predicate calculus case
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
The Description Logic Handbook
The Description Logic Handbook
ALC + T: a Preferential Extension of Description Logics
Fundamenta Informaticae - Advances in Computational Logic (CIL C08)
Rational closure for defeasible description logics
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
Preferential Reasoning for Modal Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Semantic foundation for preferential description logics
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
PTL: a propositional typicality logic
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
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One of the most successful approaches to the formalization of commonsense reasoning is the work by Lehmann and colleagues, known as the KLM approach, in which defeasible consequence relations with a preferential semantics are studied. In spite of its success, KLM is limited to propositional logic. In recent work we provided the semantic foundation for extending defeasible consequence relations to modal logics and description logics. In this paper we continue that line of investigation by going beyond the basic (propositional) KLM postulates, thereby making use of the additional expressivity provided by modal logic. In particular, we show that the additional constraints we impose on the preferential semantics ensure that the rule of necessitation holds for the corresponding consequence relations, as one would expect it to. We present a representation result for this tightened framework, and investigate appropriate notions of entailment in this context -- normal entailment, and a rational version thereof.