一个真值函项偶然逻辑的希尔伯特演算系统  

A Hilbert Calculus for Logic of Truth-Functional Contingency

作　　者：梁飞 田中旭[1] 杨新宇 Fei Liang;Zhongxu Tian;Xinyu Yang(School of Philosophy and Social Development,Shandong University;Institute of Concept and Reasoning,Shandong University)

机构地区：[1]山东大学哲学与社会发展学院 [2]山东大学概念与推理研究所

出　　处：《逻辑学研究》2021年第3期24-36,共13页Studies in Logic

基　　金：supported by “The National Social Science Fund of China”(grant number 20&ZD046);“The Fundamental Research Funds of Shandong University”(11090079614065);“Young Scholars Program of Shandong University”(11090089964225)

摘　　要：如果一个命题在经典命题逻辑中既不是一个重言式也不是一个矛盾式,则称它是真值函项偶然的。真值函项偶然逻辑即是为了刻画所有真值函项偶然的命题。本文将给出一个关于真值函项偶然逻辑的可靠且完全的希尔伯特演算。在此演算中,通过演绎所得到的公式要么是偶然公理,要么是由偶然规则推出的。A statement is truth-functionally contingent,if it is neither a tautology nor a contradiction in classical propositional logic.The logic of truth-functional contingency,is to capture all these contingent statements.In this paper,we introduce a sound and complete Hilbert calculus for the logic of truth-functional contingency,where every formula introduced in a deduction is a contingent formula,and it is introduced only if it is a contingent axiom,or it follows by one of the contingent rules of inference from contingent formulas introduced earlier in the deduction.

关 键 词：真值函项 希尔伯特 重言式 演算 逻辑 偶然 命题 

分 类 号：B81-0[哲学宗教—逻辑学]