基于n-值ukasiewicz命题逻辑的概率计量化推理系统  

A Probabilistically Quantitative Reasoning System Based on n-Valued ukasiewicz Propositional Logic

作　　者：周红军[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《模式识别与人工智能》2013年第6期521-528,共8页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.61005046);教育部高等学校博士学科点专项科研基金项目(No.20100202120012)资助

摘　　要：通过把n-值ukasiewicz命题逻辑中公式的概率真度函数抽象为模态词,把概率真度函数的基本恒等式抽象为关于模态词的公理,建立一个模态化的形式推理系统,构建其语构理论及语义理论,证明该系统关于概率真度函数的完备性定理,从而为概率计量逻辑奠定逻辑基础.The probabilistic truth degree functions of propositions in n-valued Lukaslewmz proposmonal 1ogic are abstracted as a modality, and their three basic identities are abstracted as axioms of the modality. Then, a modal logic system for reasoning about probabilistic truth degrees of propositions is proposed. The syntax and semantics are constructed. The completeness theorem with respect to probabilistic truth degree functions is finally obtained. A logic foundation is set for probabilistically quantitative logic.

关 键 词：Lukasiewicz命题逻辑 概率计量逻辑 Borel型概率真度 

分 类 号：O141[理学—数学] TP18[理学—基础数学]