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.

中文翻译：

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基于邻域语义的优先条件逻辑的统一标记演算

研究了 Burgess 引入的优先条件逻辑 PCL 及其扩展。首先，提出了一种基于邻域模型的自然语义，该模型将 Lewis 的球体模型推广到反事实逻辑。直接证明了 PCL 及其对此类模型的扩展的健全性和完整性。然后引入用于该族的所有逻辑的标记的连续演算。演算是模块化的并且具有标准的证明理论属性，其中最重要的是可采性，这需要对演算的完整性进行句法证明。通过采用通用策略，根优先证明搜索终止，从而为 PCL 及其扩展提供决策程序。最后，建立微积分的语义完备性：从失败的证明尝试中的有限分支中，可以提取根序列的有限反模型。后一个结果给出了所有考虑的逻辑的有限模型属性的建设性证明。