Monotonic modal logics
Monotonic modal logics
复制标题
单调模态逻辑
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
E. Pacuit
中科院分区：
文献类型：
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作者：
H. Hansen;C. Kupke;E. Pacuit
单调模态逻辑形成了正规模态逻辑的推广，其中菱形模态的可加性已被削弱为单调性：3p∨3q → 3(p∨q)。这种概括意味着克里普克结构不再形成足够的语义。相反，单调模态逻辑是在单调邻域结构上解释的，即邻域函数在超集下闭合的邻域结构。作为单调模态逻辑的具体例子，我们提到博弈逻辑、联盟逻辑和交替时间时序逻辑。本论文在一般框架中介绍了单调模态逻辑的结果。涵盖的主题包括模型构造和真值不变性、可定义性和对应理论、规范模型构造、代数对偶性（对于单调邻域框架）、联合代数语义、通过超合并进行克雷格插值以及通过双峰正态逻辑模拟单调模态逻辑。主要贡献是：Sahlqvist对应和正则性定理的推广，通过正则扩展对代数对偶性的详细说明，可定义框架类上Goldblatt-Thomason定理的类比，互模拟和结构等价的煤代数概念之间关系的结果，克雷格插值结果，以及保留一般框架描述性的模拟构造。
Monotonic modal logics form a generalisation of normal modal logics in which the additivity of the diamond modality has been weakened to monotonicity: 3p∨3q → 3(p∨q). This generalisation means that Kripke structures no longer form an adequate semantics. Instead monotonic modal logics are interpreted over monotonic neighbourhood structures, that is, neighbourhood structures where the neighbourhood function is closed under supersets. As specific examples of monotonic modal logics we mention Game Logic, Coalition Logic and the Alternating-Time Temporal Logic. This thesis presents results on monotonic modal logics in a general framework. The topics covered include model constructions and truth invariance, definability and correspondence theory, the canonical model construction, algebraic duality (for monotonic neighbourhood frames), coalgebraic semantics, Craig interpolation via superamalgamation, and simulations of monotonic modal logics by bimodal normal ones. The main contributions are: generalisations of the Sahlqvist correspondence and canonicity theorems, a detailed account of algebraic duality via canonical extensions, an analogue of the Goldblatt-Thomason theorem on definable frame classes, results on the relationship between bisimulation and coalgebraic notions of structural equivalence, Craig interpolation results, and a simulation construction which preserves descriptiveness of general frames.