从“帽子游戏”看模态逻辑如何表达禁自返性  

How Does Modal Logic Characterize Irreflexiveness From"Hat Game"

作　　者：陈亮[1] CHEN Liang(Hebei University,Baoding,Hebei 071100,China)

机构地区：[1]河北大学哲学与社会学学院,河北保定071100

出　　处：《贵州工程应用技术学院学报》2024年第6期63-70,共8页Journal of Guizhou University Of Engineering Science

摘　　要：“帽子游戏”形式化的核心是定义禁自返性,然而该性质无法在基本模态逻辑中得出,它可以用一阶公式表达,却没有对应的模态公式。为了在模态逻辑中表达禁自返性,逻辑学家提出了几种方案:禁自返系统就是K系统,禁自返性可以在多模态逻辑中用公式表示出来。然而,T系统包含着K系统,将K系统定义为禁自返系统会出现矛盾;多模态逻辑不具有基本模态逻辑的普遍性,使得两个方案均陷入困难。混合逻辑通过给可能世界命名,在不改变基本模态逻辑语义的基础上,能够用公式i→L¬i成功地定义禁自返性。此外,这种方法也大大提升了模态逻辑的表达力。The core of the formalization of the"hat game"is the definition of irreflexiveness,but this property cannot be derived from the basic modal logic,it can be expressed in a first-order formula,but there is no corresponding modal formula.In order to express the irreflexiveness in modal logic,logicians put forward several schemes:the irreflexive system is the K system,and the irreflexiveness can be expressed by formula in multi-modal logic.However,T system includes K system,so it would be contradictory to define K system as irreflexiveness system.Multimodal logic does not have the universality of basic modal logic,which makes both schemes difficult.By naming possible worlds,hybrid logic can successfully define irreflexiveness with the formula i→L¬i without changing the semantics of basic modal logic.In addition,this method also greatly improves the expressive power of modal logic.

关 键 词：模态逻辑 关系 禁自返性 混合逻辑 

分 类 号：B81[哲学宗教—逻辑学]