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| G?del n值命题逻辑中命题的α-真度理论 |
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李骏1,2, 王国俊1
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1.陕西师范大学,数学与信息科学学院,陕西,西安,710062;2.兰州理工大学,理学院,甘肃,兰州,730050
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| 摘要: |
| 为了在n值命题逻辑系统中建立一种程度化推理机制,并为其提供一个可能的近似推理框架,利用势为n的均匀概率空间的无穷乘积,在n值G?del命题逻辑系统中引入命题的α-真度概念.证明了一般真度推理规则,给出了判定α-重言式的充分必要条件,并利用命题的α-真度定义了命题间的α-相似度,进而导出命题集上的一种伪距离,使得在n值命题逻辑系统中展开近似推理成为可能.提出的程度化推理方法为近似推理的算法实现奠定了基础,并对知识推理的程度化有所启示. |
| 关键词: α-真度 真度 α-相似度 伪距离 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.10331010 (国家自然科学基金); the Innovation Foundation for Doctors of Shaanxi Normal University of China (陕西师范大学博士创新基金); the Outstanding Youth Foundation of Lanzhou University of Technology of China (兰州理工大学优秀青年基金) |
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| Theory of α-Truth Degrees in n-Valued G?del Propositional Logic |
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LI Jun,WANG Guo-Jun
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| Abstract: |
| In order to establish a graded reasoning mechanism and provide a possible framework for approximate reasoning in n-valued propositional logic, this paper introduces the concept of α-truth degrees of propositions in n-valued Gdel logical system by using the infinite product of uniformly distributed probability spaces of cardinal n. It is proved that the general inference rules with truth degrees hold, and a sufficient and necessary condition to judge α-tautology is obtained. Moreover, an intrinsic pseudo-metric on the set of propositions is defined by means of the similarity degree between propositions, which makes it possible to develop approximate reasoning in n-valued propositional logic. The graded method proposed in this paper lays a foundation for the algorithmic realization of approximate reasoning and serves as a guideline for the graded reasoning about knowledge. |
| Key words: α-truth degree truth degree α-similarity degree pseudo-metric |
