Elementary canonical formulae: extending Sahlqvist's theorem
Elementary canonical formulae: extending Sahlqvist's theorem
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基本规范公式：扩展 Sahlqvist 定理
DOI：
10.1016/j.apal.2005.10.005
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
D. Vakarelov
中科院分区：
文献类型：
--
作者：
V. Goranko;D. Vakarelov
我们推广和扩展的Sahlqvist公式类在任意的polyadic模态语言，所谓的归纳公式类。为了介绍它们，我们使用一个表示模态polyadic语言在组合风格，因此，特别是，开发我们认为是一个更好的句法方法，以小学规范公式。通过推广Sahlqvist-van Benthem的极小赋值方法和Sambin和Vaccaro的拓扑方法，我们证明了所有的归纳公式都是初等规范的，从而推广了Sahlqvist定理。特别是，我们给出了一个简单的例子，归纳公式，这是不是框架等价于任何Sahlqvist公式。然后，经过更深入的分析，归纳公式作为集理论运营商在描述性和Kripke框架，我们建立了一个更强的模型理论表征这些公式在一个合适的等价语法简单的公式（“原始正则公式”）在语言的扩展与反向模态。最后，我们研究并刻画了具有名词的可逆语言中的初等规范公式，其中相关的持久性概念是关于离散框架的。
We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae (‘primitive regular formulae’) in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames.