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Defeasible Entailment: from Rational Closure to Lexicographic Closure and Beyond
Casini, Giovanni; Meyer, Thomas; Varzinczak, Ivan
2018In Proceeding of the 17th International Workshop on Non-Monotonic Reasoning (NMR 2018)
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Keywords :
nonmonotonic logics; conditional logics; defeasible reasoning
Abstract :
[en] In this paper we present what we believe to be the first systematic approach for extending the framework for de- feasible entailment first presented by Kraus, Lehmann, and Magidor—the so-called KLM approach. Drawing on the properties for KLM, we first propose a class of basic defea- sible entailment relations. We characterise this basic frame- work in three ways: (i) semantically, (ii) in terms of a class of properties, and (iii) in terms of ranks on statements in a knowlege base. We also provide an algorithm for computing the basic framework. These results are proved through vari- ous representation results. We then refine this framework by defining the class of rational defeasible entailment relations. This refined framework is also characterised in thee ways: se- mantically, in terms of a class of properties, and in terms of ranks on statements. We also provide an algorithm for com- puting the refined framework. Again, these results are proved through various representation results. We argue that the class of rational defeasible entail- ment relations—a strengthening of basic defeasible entail- ment which is itself a strengthening of the original KLM proposal—is worthy of the term rational in the sense that all of them can be viewed as appropriate forms of defeasi- ble entailment. We show that the two well-known forms of defeasible entailment, rational closure and lexicographic clo- sure, fall within our rational defeasible framework. We show that rational closure is the most conservative of the defeasi- ble entailment relations within the framework (with respect to subset inclusion), but that there are forms of defeasible en- tailment within our framework that are more “adventurous” than lexicographic closure.
Disciplines :
Computer science
Author, co-author :
Casini, Giovanni ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Meyer, Thomas;  University of Cape Town > Computer Science
Varzinczak, Ivan;  Universite d'Artois > CRIL > maitre de conference
External co-authors :
yes
Language :
English
Title :
Defeasible Entailment: from Rational Closure to Lexicographic Closure and Beyond
Publication date :
2018
Event name :
17th International Workshop on Non-Monotonic Reasoning (NMR 2018)
Event place :
Tempe, United States - Arizona
Event date :
27-29 October 2018
Audience :
International
Main work title :
Proceeding of the 17th International Workshop on Non-Monotonic Reasoning (NMR 2018)
Pages :
109-118
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
European Projects :
H2020 - 690974 - MIREL - MIREL - MIning and REasoning with Legal texts
Funders :
CE - Commission Européenne [BE]
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since 22 November 2018

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