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