中介命题逻辑的一种无穷值语义模型及其意义  

Model of Infinite Valued of Medium Proposition Logic

作　　者：潘正华[1] 

机构地区：[1]江南大学理学院数理研究所,无锡214122

出　　处：《计算机研究与发展》2008年第z1期158-164,共7页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(60575038)

摘　　要：中介逻辑(medium logic,ML)自建立了它的三值语义模型后,ML就被许多学者认定为三值逻辑.对于中介逻辑核心理论的中介命题逻辑系统,给出一种真值域为[0,1]的无穷值语义模型,研究了它的性质,并证明了中介命题逻辑在此模型下具有可靠性与完备性.此模型的存在表明,认定中介逻辑是一种三值逻辑的理由是不充分的.该模型更适合反映中介逻辑的基本思想,而且为中介逻辑在其他领域的应用提供了一个基础.Medium proposition logic(MP) is one kind of non-classical logic. The semantic characteristic on MP, three-valued model had been given in the past, so many scholars(include founders) affirm that MP is one kind of three-valued logic. But to affirmed MP be three-valued logic, ought to proving that MP does not exist other models based on the model theory, such as the intuitionist proposition logic have classical model, but intuitionist proposition logic is not classical logic. This paper set up a model of infinite valued of MP, some properties of the model are studied, and the theorems of completeness and reliability are proved. The model not only rightly depicts the medium principle which basic idea of MP, but also show that 'medium proposition logic is one kind of three valued logic' is incorrect, and offered a base for more application of MP.

关 键 词：中介命题逻辑 三值模型 有穷和无穷值模型 完备性 可靠性 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]