六元语言真值模态命题逻辑及其归结自动推理研究
6-Element Linguistic Truth-Valued Modal Proposition Logic and Resolution Automated Reasoning
DOI: 10.12677/CSA.2022.125141, PDF,   
作者: 王诗慧：辽宁师范大学，数学学院，辽宁 大连；王艳芳：辽阳职业技术学院，计算机科学系，辽宁 辽阳；崔晓松*：辽宁师范大学，计算机与信息技术学院，辽宁 大连
关键词: 六元语言真值格蕴涵代数；模态命题逻辑；归结原理；6-Element Linguistic Truth-Valued Lattice Implication Algebra； Modal Proposition Logic； Resolution Principle
摘要: 在日常生活中，人们通常使用自然语言进行推理和判断。为了将格值模态命题逻辑更好地应用于实际中，本文提出了以六元语言真值格蕴涵代数为真值域的六元语言真值模态命题逻辑系统，定义一个将公式集和可能世界集映射到六元语言真值格蕴涵代数上的赋值映射，讨论其运算及性质，并探讨该系统基于滤子的归结原理。提出计算归结式的规则以及基于滤子的归结方法，并通过一个例子说明该方法的合理性。该系统不仅可以处理全序性信息，也可以处理非全序性信息。
Abstract: In daily life, people usually use natural language to reason and judge. In order to better apply lattice-valued modal propositional logic in practice, a 6-element linguistic truth-valued modal propositional logic system with the 6-element linguistic truth-valued lattice implication algebra as the true value domain is proposed. An evaluation map that maps the set of formulas and the set of possible worlds to 6-element linguistic truth-valued lattice implication algebra is defined, and its operations and properties are analyzed. The resolution principle based on filter is discussed. The rules for calculating the resolution formulas and the resolution method based on filter are proposed, and an example is used to illustrate the rationality of the method. The system can process not only comparable information, but also incomparable information.
文章引用：王诗慧, 王艳芳, 崔晓松. 六元语言真值模态命题逻辑及其归结自动推理研究[J]. 计算机科学与应用, 2022, 12(5): 1413-1424. https://doi.org/10.12677/CSA.2022.125141

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