Cut-Free Gentzen Sequent Calculi for Tense Logics

被引：0

作者：

Lin, Zhe ^{[1
]}

Ma, Minghui ^{[2
]}

机构：

[1] Xiamen Univ, Dept Philosophy, Xiamen 361000, Peoples R China

[2] Sun Yat Sen Univ, Inst Logic & Cognit, Dept Philosophy, Guangzhou 510275, Peoples R China

来源：

AXIOMS | 2023年 / 12卷 / 07期

关键词：

proof theory; tense logic; sequent calculus; cut elimination;

D O I：

10.3390/axioms12070620

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The cut-free single-succedent Gentzen sequent calculus GKt for the minimal tense logic K-t is introduced. This sequent calculus satisfies the displaying property. The proof proceeds in terms of a Kolmogorov translation and three intermediate sequent systems. Finally, we show that tense logics axiomatized by strictly positive implication have cut-free Gentzen sequent calculi uniformly.

引用

页数：19

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