Abstract

Conditional logic is a kind of modal logic for analyzing the truth conditions and inferences of conditional sentences in natural language. However, it has been pointed out in the literature that empirical problems plague all of the previously proposed conditional logics. Moreover, C1 and C2 are defined by imposing certain restrictions on their Kripke frames, and there exist no corresponding proof systems. In order to solve these problems, we propose a new system of conditional logic, which we call Cb. Cb is an extension of C+ through the addition of new rules on accessibility, and it has a corresponding tableau system. We show that Cb has empirical advantages over C1 and C2 as a model of inference in natural language, and compare it with other proof systems of conditional logic.