A standard internal calculus for Lewis’ counterfactual logics

Abstract

The logic V is the basic logic of counterfactuals in the family of Lewis’ systems. It is characterized by the whole class of so-called sphere models. We propose a new sequent calculus for this logic. Our calculus takes as primitive Lewis’ connective of comparative plausibility ≤: a formula A ≤ B intuitively means that A is at least as plausible as B. Our calculus is standard in the sense that each connective is handled by a finite number of rules with a fixed and finite number of premises. Moreover our calculus is “internal”, in the sense that each sequent can be directly translated into a formula of the language. We show that the calculus provides an optimal decision procedure for the logic V.