What Does Entailment for PTL Mean?

Richard Booth, Giovanni Casini, Thomas Meyer, Ivan Varzinczak
unpublished
We continue recent investigations into the problem of reasoning about typicality. We do so in the framework of Propo-sitional Typicality Logic (PTL), which is obtained by enriching classical propositional logic with a typicality operator and characterized by a preferential semanticsàsemantics'semanticsà la KLM. In this paper we study different notions of entailment for PTL. We take as a starting point the notion of Rational Closure defined for KLM-style conditionals. We show that the additional
more » ... ex-pressivity of PTL results in different versions of Rational Closure for PTL-versions that are equivalent with respect to the conditional language originally proposed by KLM.
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