基于语言真值格蕴涵代数中对偶分子的推理性质  

The Reasoning Properties of Dual Molecule in Linguistic Truth-valued Lattice Implication Algebra

作　　者：赖家俊[1,2] 徐扬[1] 

机构地区：[1]西南交通大学智能控制开发中心,四川成都610031 [2]西南交通大学信息科学与技术学院,四川成都610031

出　　处：《模糊系统与数学》2010年第2期1-6,共6页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(60875034);教育部博士点专项基金资助项目(20060613007)

摘　　要：众所周知,代数结构已成功应用于经典与非经典逻辑中。沿袭这种思想,徐扬教授为语言真值格值命题逻辑的代数语义解释找到了一个语言真值格蕴涵代数(L-LIA)的方法。本文进一步研究L-LIA中对偶分子的推理性质,证明了对偶分子在一定程度上对算子∨、∧、→具有闭性,得到了一些有趣的新结果,特别是给出了它的一些推理性质,并验证了在Lv(9×2)中的相应结果,进而对蕴涵进行了拓展,得到了预线性性的逻辑推理性质,并证明了此推理性质的正确性。It is well known that algebraically structure has been successfully applied to classical and non-classical logics. Following this direction, an L-LIA approach to the problem of finding out a tool to describe algebraic semantics of linguistic truth-valued lattice value propositional logic has been introduced by Prof. Yang Xu. This paper further discusses the reasoning properties of dual molecule in L-LIA, are introduced and it is proved that operators V,∧,→ have some degree closed, some new results are revealed. In particular, the inference properties of dual molecule are given, and the correspondence results of v（9×2） are also provided. Moreover, we obtain the logical inference properties in pre-linear based on dual molecule to implication, and we show that the inference properties can be proved.

关 键 词：语言真值蕴涵代数 对偶分子 推理性质 闭性 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O159[自动化与计算机技术—控制科学与工程]