What Does Entailment for PTL Mean?

Booth, Richard (Mahasarakham University) | Casini, Giovanni (University of Pretoria) | Meyer, Thomas (University of Pretoria) | Varzinczak, Ivan José (Universidade Federal do Rio de Janeiro)

AAAI Conferences 

We continue recent investigations into the problem of reasoning about typicality. We do so in the framework of Propositional Typicality Logic (PTL), which is obtained by enriching classical propositional logic with a typicality operator and characterized by a preferential semantics à 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 expressivity 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.