Rules of Inference in Lattice-Valued Propositional Logic Lvpl
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摘要: 为描述取小、多重推理、多维推理等实际推理方法,在格值命题逻辑系统Lvpl中,引入了几类相应的推理规则.这些推理规则由语法和语义两部分组成,且在两部分之间存在一定的协调水平.证明了对于适当的语法语义协调水平,当Lvpl的公式集的L型模糊集为同态映射时,它们关于这几类推理规则都在一定程度上封闭.Abstract: To describe reasoning methods such as minimizing,multiple reasoning,multi-dimensional reasoning etc.,corresponding rules of inference in lattice-valued propositional logic Lvpl are introduced.These rules are composed of two parts,semantics and syntax,and there exists a certain consistency between the two parts.It is proved that,with an appropriate level of consistency between semantics and syntax,L-type fuzzy subsets of the set of all formulae of Lvpl are closed to a certain extent with respect to these rules of inference when they are homomorphic.
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Key words:
- lattice-valued propositional logic /
- rules of inference /
- closeness /
- syntax /
- semantics
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