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The preferential conditional logic PCL, introduced by Burgess, and itsextensions are studied. First, a natural semantics based on neighbourhoodmodels, which generalise Lewis' sphere models for counterfactual logics, isproposed. Soundness and completeness of PCL and its extensions with respect tothis class of models are proved directly. Labelled sequent calculi for alllogics of the family are then introduced. The calculi are modular and havestandard proof-theoretical properties, the most important of which isadmissibility of cut, that entails a syntactic proof of completeness of thecalculi. By adopting a general strategy, root-first proof search terminates,thereby providing a decision procedure for PCL and its extensions. Finally, thesemantic completeness of the calculi is established: from a finite branch in afailed proof attempt it is possible to extract a finite countermodel of theroot sequent. The latter result gives a constructive proof of the finite modelproperty of all the logics considered.

Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics