We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and completeness with respect to the semantics. Then, we introduce two kinds of analytic proof systems for several logics in the family: a multi-premisses sequent calculus in the style of Lellmann and Pattinson, for which we prove cut admissibility, and a hypersequent calculus based on structured calculi for conditional logics by Girlando et al., tailored for countermodel construction over failed proof search. Our results constitute the first steps in the definition of a unified proof theoretical framework for logics equipped with a comparative plausibility operator.
翻译:我们引入了一套比邻模式比较合理逻辑的体系,将刘易斯比较合理逻辑操作员比球体模型普遍化。我们为逻辑提供了轴心系统,并证明了这些逻辑在语义学方面的正确性和完整性。然后,我们为家庭的若干逻辑引入了两种分析性证据系统:一种是莱尔曼和帕特廷森风格的多前导序列计算法,我们可以证明它具有可接受性,另一种是高序列计算法,它基于Girrando等人对有条件逻辑的结构计算法,为反模范的搜索与失败的证据搜索相适应。我们的结果构成了为具有比较合理性操作员的逻辑定义统一证据理论框架的第一步。