Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics

Abstract The preferential conditional logic $ \mathbb{PCL} $, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalizes Lewis’ sphere models for counterfactual logics, is proposed. Soundness completeness of with respect to this class proved directly. Labelled sequent calculi all logics the family then introduced. modular have standard proof-theoretical properties, most important admissibility cut that entails syntactic proof calculi. By adopting general strategy, root-first search terminates, thereby providing decision procedure extensions. Finally, semantic established: from finite branch in failed attempt it possible extract countermodel root sequent. latter result gives constructive model property considered.