A logical framework for default reasoning
Artificial Intelligence
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
What does a conditional knowledge base entail?
Artificial Intelligence
Preferential reasoning in the perspective of Poole default logic
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
A correspondence theory for terminological logics: preliminary report
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
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)
A defeasible reasoning approach for description logic ontologies
Proceedings of the South African Institute for Computer Scientists and Information Technologists Conference
PTL: a propositional typicality logic
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
Normal modal preferential consequence
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
Defeasible inheritance-based description logics
Journal of Artificial Intelligence Research
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Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching description logics with non-monotonic reasoning capabilities, especially preferential reasoning as developed by Lehmann and colleagues in the 90's, would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in description logics. In this paper we fill this gap by providing a natural and intuitive semantics for defeasible subsumption in the description logic $\mathcal{ALC}$ . Our semantics replaces the propositional valuations used in the models of Lehmann et al.. with structures we refer to as concept models . We present representation results for the description logic $\mathcal{ALC}$ for both preferential and rational consequence relations. We argue that our semantics paves the way for extending preferential and rational consequence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of first-order relational structures.