| 李骏,李尧龙,黎锁平.逻辑系统$G_3$中命题的真度值之集在[0,1]上的分布[J].数学研究及应用,2006,26(3):605~612 |
| 逻辑系统$G_3$中命题的真度值之集在[0,1]上的分布 |
| Theory of Truth Degrees in G\"{o}del 3-Valued Propositional Logic |
| 投稿时间：2004-03-28 |
| DOI：10.3770/j.issn:1000-341X.2006.03.027 |
| 中文关键词: 真度 真度推理规则 稠密. |
| 英文关键词:truth degree inference rule with truth degree dense. |
| 基金项目:甘肃省自然科学基金(ZS032-B52-031),兰州理工大学优秀青年基金 |
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| 中文摘要: |
| 利用势为3的均匀概率空间的无穷乘积在G\"{o}del三值命题逻辑中引入了公式的真度概念,给出了真度推理规则,证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式,为进一步建立三值命题逻辑的近似推理理论奠定了基础. |
| 英文摘要: |
| Base on the infinite product of evenly distributed probability space, this paper introduces the theory of truth degrees in G\"{o}del 3-valued propositional logic and inference rules with truth degrees are given. Moreover, it is proved that the set of truth degrees of propositions is dense in [0,1], and expressions of truth degrees are obtained. This paves the way for the further study on approximate reasoning. |
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