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On rational entailment for Propositional Typicality Logic

Booth, Richard, Casini, Giovanni, Meyer, Thomas and Varzinczak, Ivan 2019. On rational entailment for Propositional Typicality Logic. Artificial Intelligence 277 , 103178. 10.1016/j.artint.2019.103178

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Abstract

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 sen- tence 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 mono- tonic 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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Publisher: Elsevier
ISSN: 0004-3702
Date of First Compliant Deposit: 7 October 2019
Date of Acceptance: 25 September 2019
Last Modified: 20 Jan 2021 09:15
URI: http://orca.cardiff.ac.uk/id/eprint/125890

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