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首页> 外文期刊>Journal of logic and computation >Notions of Bisimulation for Heyting-Valued Modal Languages
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Notions of Bisimulation for Heyting-Valued Modal Languages

机译：Heyting值模态语言的双仿真概念

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摘要

We examine the notion of bisimulation and its ramifications, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We define two notions of bisimulation that allow us to obtain truth invariance results. We provide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulae and prove a Hennessy-Milner-type theorem. If the underlying algebra H is finite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our definitions and results draw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.
机译：我们在M.Fitting引入的Heyting值模态语言家族的背景下研究了双仿真的概念及其后果。该族中的每种模态语言都基于真实值的基础空间，即Heyting代数H。所有真实值均直接用该语言表示，该语言在具有H值可及性关系的关系框架上进行解释。我们定义了双仿真的两个概念，它们使我们能够获得真理不变性结果。我们提供游戏语义，并且对于更有趣和更复杂的概念，我们能够提供特征公式并证明Hennessy-Milner型定理。如果基础代数H是有限的，则可以使用许多相关专家将Heyting值模态模型等效地重构为与认知情况相关的形式。我们的定义和结果从这种表述中得到启发，而这种表述是知识表示应用程序的独立利益。

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