Epistemic Conditionals and the Logic of Subsets

Abstract

This paper proposes a formalization of conditional reasoning using Moss and Parikh’s logic of subsets so that a reasoner can express both conditional assertions about beliefs, as well as beliefs about conditional assertions. We present a complete axiomatization of the logic and show that it is decidable. A version of the Ramsey test is found to be compatible with this logic and provides a correspondence between conditionals and belief contraction.