Contextual conditional reasoning

We extend the expressivity of classical conditional reasoning by introducing context as a new parameter. The enriched conditional logic generalises the defeasible conditional setting in the style of Kraus, Lehmann, and Magidor, and allows for a refined semantics that is able to distinguish, for example, between expectations and counterfactuals. In this paper we introduce the language for the enriched logic and define an appropriate semantic framework for it. We analyse which properties generally associated with conditional reasoning are still satisfied by the new semantic framework, provide a suitable representation result, and define an entailment relation based on Lehmann and Magidor's generally-accepted notion of Rational Closure.