摘要
从结构推理的观点来看,结合演算是一种很弱的逻辑,因为它仅容纳一种结构规则,即"结合规则"。正结合演算作为一种"正命题逻辑",是结合演算的基础。本文构建了正结合演算结构推理系统BL和对应的公理系统B,阐述了结合演算拒斥"交换规则"、"收缩规则"和"弱化规则"的理论意义和应用价值,证明了系统BL和系统B的等价性。
From the viewpoint of structural inference, associative calculus is a very weak logic, because it only contains one kind of structural rule, namely ＂associative rule＂. As a kind of positive propositional logic, positive associative calculus is the basis of associative calculus. This paper constructs structural reasoning system BL of positive associative calculus and its corresponding axiomatic system B, expounds theoretical significance and practical value of rejecting ＂commutative rule＂, ＂contraction rule＂ and ＂weakening rule＂ in the calculus, and proves that the system BL is equivalent to the system B.
出处
《逻辑学研究》
CSSCI
2012年第4期1-15,共15页
Studies in Logic
基金
教育部人文社会科学重点研究基地重大项目<结构推理及其应用研究>(10JJD720010)
国家社会科学基金<谓词逻辑与元逻辑研究>(11BZX063)
