一类命题逻辑的一般弱框架择类语义  

Class-selection Semantics on General Weak Frames for a Class of Propositional Logics

作　　者：冯棉[1] 

机构地区：[1]华东师范大学哲学系

出　　处：《逻辑学研究》2011年第2期20-34,共15页Studies in Logic

基　　金：教育部人文社会科学重点研究基地重大项目<结构推理及其应用研究>(10JJD720010)

摘　　要：命题逻辑的一般弱框架择类语义是相干邻域语义的变形,其特点是:采用择类运算来刻画逻辑常项;语义运算与逻辑联结词之间有清晰的对应关系,可以从整体上处理一类逻辑,具有普适性。本文将这种语义用于一类B、C、K、W命题逻辑,包括相干逻辑R及其线性片段、直觉主义逻辑及其BCK片段等,并借助典范框架和典范赋值,证明了这些逻辑系统的可靠性和完全性。Class-selection semantics on general weak frames of prepositional logics is a transformation of relevant neighborhood semantics.Characteristically,it employs class-selection operations to describe logical constants,and the resulting clear corresponding relations between semantic operations and logical connectives can properly deal with a class of logics as a whole,with general applicability.This paper applies such semantics to a class of propositional logics with B,C,K or W,including relevant logic R and its linear fragment,intuitionistic propositional logic and its BCK fragment,etc.It also proves the soundness and completeness of these logical systems by canonical frame and canonical valuation.

关 键 词：结构规则 相干逻辑 线性片段 直觉主义逻辑 BCK片段 一般弱框架择类语义 

分 类 号：B812[哲学宗教—逻辑学]