基于互模拟的模态逻辑与非良基集合论之间的关系

首先介绍模态逻辑的两种语义:克里普克模型和非良基集合模型,表明这两种语义的相互可推演性,证明非良基模型,描述互模拟等价的克里普克模型类;接着,从模型的视角讨论集合上的互模拟与模态等价的关系;最后,运用互模拟和集合翻译等概念讨论非良基集合与模态逻辑的关系,证明:"一个集合论公式在集合上的互模拟下是不变的当且仅当它等价于一个模态公式的标准集合论翻译"。

The Relationship between Modal Logic and Non-Well-Founded Set Theory Basing on Bisimulation

Firstly,it introduces and set-theoretic semantics of modal logics and Kripke semantics,shows we can deduce one of the two semantics from the other,and proves that non-founded models can be seen as representing bisimulation equivalence classes of Kripke models.Next,it discusses the relationship between bisimulation upon set theory and modal equivalence in view of model;Finally,it discusses the telationship between modal languages and set-theoretic language by means of some notions including bisumulation and set interpretation,and proves "a set theory formula is invariant for bisimulation upon sets iff it is equivalent to the standard set theory translation of a modal formula".