A labelled tableau calculus for nonmonotonic (cumulative) consequence relations

Abstract

In this paper we present a labelled proof method for computing non monotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the propositional system KE+ -atableau-like analytic proof system devised to be used both as a refutation and a direct method of proof- enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications. © Springer-Verlag Berlin Heidelberg 2000.