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See detailOn the Entailment Problem for a Logic of Typicality
Booth, Richard UL; Casini, Giovanni UL; Meyer, Thomas et al

in Yang, Qiang; Wooldridge, Michael (Eds.) Proceedings of the TwentyFourth International Joint Conference on Artificial Intelligence. Buenos Aires, Argentina, 25–31 July 2015 (2015)

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. In spite of the non-monotonic features introduced by the ... [more ▼]

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. 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. We investigate different (semantic) versions of entailment for PTL, based on the notion of Rational Closure as defined by Lehmann and Magidor for KLM-style conditionals, and constructed using minimality. 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 define two primary forms of entailment for PTL and discuss their advantages and disadvantages. [less ▲]

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See detailA non-classical logical foundation for naturalised realism
Ruttkamp-Bloem, Emma; Casini, Giovanni UL; Meyer, Thomas

in Arazim, Pavel; Dančák, michal (Eds.) The Logica Yearbook (2015)

Detailed reference viewed: 74 (4 UL)