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TABULARITY AND POST-COMPLETENESS IN TENSE LOGIC

Part of: General logic

Published online by Cambridge University Press:  07 April 2022

QIAN CHEN  and
MINGHUI MA
QIAN CHEN
Affiliation:
TSINGHUA-AMSTERDAM JOINT RESEARCH CENTRE FOR LOGIC DEPARTMENT OF PHILOSOPHY TSINGHUA UNIVERSITY NO. 1 QINGHUA YUAN, HAIDIAN DISTRICT BEIJING 100084, CHINA E-mail: [email protected]
MINGHUI MA*
Affiliation:
INSTITUTE OF LOGIC AND COGNITION DEPARTMENT OF PHILOSOPHY SUN YAT-SEN UNIVERSITY NO. 135 XINGANG XI ROAD, HAIZHU DISTRICT GUANGZHOU 510275, CHINA
*
E-mail: [email protected]
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Abstract

A new characterization of tabularity in tense logic is established, namely, a tense logic L is tabular if and only if $\mathsf {tab}_n^T\in L$ for some $n\geq 1$. Two characterization theorems for the Post-completeness in tabular tense logics are given. Furthermore, a characterization of the Post-completeness in the lattice of all tense logics is established. Post numbers of some tense logics are shown.

Keywords

Tense logictabularitypost-completeness

MSC classification

Primary: 03B44: Temporal logic
Secondary: 03B45: Modal logic (including the logic of norms)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 2 , June 2024 , pp. 475 - 492
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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