关于认知似然性模型的模型论
Some Remarks on the Model Theory of Epistemic Plausibility Models
摘要：
经典的知识和信念逻辑通常是在克里普克模型上解释的，对于克里普克模型，数学上发展良好的模型理论是可用的。然而，这种模型不足以捕捉动态现象。因此，引入了认知可解释性模型。因为这些模型的结构比Kripke模型丰富得多，所以它们并不直接继承模态逻辑的模型理论结果。因此，虽然认知可解释性结构非常适合建模的目的，广泛的调查，他们的模型理论一直缺乏到目前为止。本文的目的正是填补这一空白，通过启动一个系统的探索模型理论的认知可解释性模型。与“普通”模态逻辑一样，重点将放在互模拟的概念上。我们定义了各种概念的互模拟（参数化的语言L），并表明L-双相似意味着L-等价。我们证明了一个Hennesy-Milner型结果和两个不可定义性结果。然而，我们的主要观点是一个负面的，即互模拟不能简单地推广到认知可验证性模型，如果考虑到条件信念。我们提出了两种方法来处理这个问题：（i）增加一个模态的语言，和（ii）把额外的限制模型。最后，我们对互模拟和动态模型变化之间的相互作用做了一些评论。
英文摘要：
Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic plausibility models have been introduced. Because these are much richer structures than Kripke models, they do not straightforwardly inherit the model-theoretical results of modal logic. Therefore, while epistemic plausibility structures are well-suited for modeling purposes, an extensive investigation of their model theory has been lacking so far. The aim of the present paper is to fill exactly this gap, by initiating a systematic exploration of the model theory of epistemic plausibility models. Like in 'ordinary' modal logic, the focus will be on the notion of bisimulation. We define various notions of bisimulations (parametrized by a language L) and show that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type result, and also two undefinability results. However, our main point is a negative one, viz. that bisimulations cannot straightforwardly be generalized to epistemic plausibility models if conditional belief is taken into account. We present two ways of coping with this issue: (i) adding a modality to the language, and (ii) putting extra constraints on the models. Finally, we make some remarks about the interaction between bisimulation and dynamic model changes.
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