Non-Analytic Tableaux for Chellas's Conditional Logic CK and Lewis's Logic of Counterfactuals VC

TL;DR

This paper develops tableau calculi for Chellas's CK and Lewis's VC conditional logics by extending Priest's existing system, highlighting the role of the cut rule for completeness.

Contribution

It introduces new tableau rules for CK and VC logics, building on Priest's calculus, and analyzes their completeness conditions.

Findings

Tableau calculi for CK and VC are established.

Completeness depends on the cut rule.

Extensions of Priest's system are effective for these logics.

Abstract

Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.