语境同义性逻辑

众所周知,基于可能世界语义的内涵逻辑由于对意义的刻画过于粗粝而导致了所谓的"超内涵问题".为了解决超内涵问题,出现了各种超内涵逻辑,其中由Suszko提出的带等词的命题逻辑(SCL)是超内涵逻辑中最基本的一种.本文是对SCL的精炼,其动机是语境同义性论题(CST).该论题认为,同义性标准具有语境依赖性.基于认知语境主义,我们给出了CST的一个论证.通过将,SCL中的二元等词修改为一个三元结构,用来表示两个陈述相对某个语境表达同一命题,我们给出了CST的希尔伯特式公理系统.我们证明了该系统相对一个代数模型类是可靠的和完全的.该代数模型的论域由命题构成,同时附带一组命题上的全等关系,用以刻画相对于语境的命题同一性.我们运用该逻辑部分解决了分析悖论这一困扰逻辑学家多年的问题.与我们之前的基于相同动机的论文17]相比,本文给出的形式语言更加丰富,从而能够表达不同语境之间以及不同语境的同义性之间的关系.

A Logic of Contextual Synonymy

It is well-known that intensional logics based on possible worlds semantics are too coarse-grained to characterize meanings, which causes the so-called 'hyperintensional problem'. To solve the problem, a lot of hyperintensional logics have been proposed, among which Suszko's sentential calculus with identity connective (SCL) is a fundamental one. This paper is a refinement of SCL motivated by the contextual synonymy thesis (CST), arguing that the standard of synonymy is context-dependent. We give an argument of CST using the popular theory of epistemical contextualism. Then we provide a Hilbert-style axiomatization of CST, by modifying Suszko's binary connective to a ternary construction representing that two statements express the same proposition with respect to a given context. We prove the soundness and completeness of the logic with respect to a class of algebraic models, where the universe consists of propositions and is supplied with a group of congruence relations on it modeling the contextual prepositional identity. We also show how the logic can be applied to give a partial solution to the paradox of analysis, which has baffled logicians for a long time. Compared to our previous work 17], the formal language given in this paper is richer so that the relation between different contexts as well as the the relation of synonymy between them can be expressed.