Reference : On Rational Entailment for Propositional Typicality Logic
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Engineering, computing & technology : Computer science
Computational Sciences
On Rational Entailment for Propositional Typicality Logic
Casini, Giovanni mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Meyer, Thomas mailto [University of Cape Town > Computer Science > > full professor]
Varzinczak, Ivan mailto [Universite d'Artois > CRIL > > maitre de conference]
Booth, Richard mailto [Cardiff University > Computer Science > > Lecturer]
[en] nonmonotonic logics ; modal logics ; defeasible reasoning
[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.
H2020 ; 690974 - MIREL - MIREL - MIning and REasoning with Legal texts

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