Abstract

Conditional logic is the deductive system , where is the set of propositional connectives {, ,} and is the structural finitary consequence relation on the absolutely free algebra that preserves degrees of truth over the structure of truth values C, . HereC is the non-commutative regular extension of the 2-element Boolean algebra to 3 truth values {t, u, f}, andfut. In this paper we give a Gentzen type axiomatization for conditional logic.