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On Rational Entailment for Propositional Typicality Logic
Casini, Giovanni; Meyer, Thomas; Varzinczak, Ivan et al.
2018
 

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Keywords :
nonmonotonic logics; modal logics; defeasible reasoning
Abstract :
[en] Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence holds. The semantics of PTL is in terms of ranked models as studied in the well-known KLM approach to preferential reasoning and therefore KLM-style rational consequence relations can be embedded in PTL. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate in many contexts. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we investigate three different (semantic) versions of entailment for PTL, each one based on the definition of rational closure as introduced by Lehmann and Magidor for KLM-style conditionals, and constructed using different notions of minimality.
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 > full professor
Varzinczak, Ivan;  Universite d'Artois > CRIL > maitre de conference
Booth, Richard;  Cardiff University > Computer Science > Lecturer
Language :
English
Title :
On Rational Entailment for Propositional Typicality Logic
Publication date :
2018
Publisher :
ArXiv
Report number :
1809.10946
Number of pages :
27
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 December 2018

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