Beyond Rank 1: Algebraic Semantics and Finite Models for Coalgebraic Logics
Beyond Rank 1: Algebraic Semantics and Finite Models for Coalgebraic Logics
复制标题
超越排名 1：代数语义和代数逻辑的有限模型
DOI：
10.1007/978-3-540-78499-9_6
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Lutz Schröder
中科院分区：
文献类型：
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作者：
D. Pattinson;Lutz Schröder
Colgebras为大型（主要是非正态）模态逻辑的语义提供了一个统一的框架，包括例如单调模态逻辑，概率和分级模态逻辑以及联盟逻辑以及模态逻辑的通常的Kripke语义。在较早的工作中，已建立了W.R.T.的有限模型属性。所有适合当前给定逻辑的结构的类别；相应的模态逻辑的特征是在等级1（即没有嵌套模态）中进行公理。在这里，我们扩展了煤层技术的范围，以覆盖逻辑，这些逻辑在其模型上强加了全局特性，该逻辑是在逻辑方面具有可能嵌套方式的框架条件（在Kripke框架上的对称条件或传递性等框架条件的概括中）））） 。我们表明，此类逻辑的有限模型属性遵循复杂代数相关类别的有限代数属性，然后研究有限代数属性的足够条件。示例应用程序包括联盟逻辑的扩展以及不确定性和知识的逻辑。
Coalgebras provide a uniform framework for the semantics of a large class of (mostly non-normal) modal logics, including e.g. monotone modal logic, probabilistic and graded modal logic, and coalition logic, as well as the usual Kripke semantics of modal logic. In earlier work, the finite model property for coalgebraic logics has been established w.r.t. the class of all structures appropriate for a given logic at hand; the corresponding modal logics are characterised by being axiomatised in rank 1, i.e. without nested modalities. Here, we extend the range of coalgebraic techniques to cover logics that impose global properties on their models, formulated as frame conditions with possibly nested modalities on the logical side (in generalisation of frame conditions such as symmetry or transitivity in the context of Kripke frames). We show that the finite model property for such logics follows from the finite algebra property of the associated class of complex algebras, and then investigate sufficient conditions for the finite algebra property to hold. Example applications include extensions of coalition logic and logics of uncertainty and knowledge.