Pretabular Tense Logics over S4t

Authors: Qian Chen
To appear in: Annals of Pure and Applied Logic. arXiv:2412.19558

Abstract

This paper studies pretabular tense logics in the lattice $\mathsf{NExt}(\mathsf{S4}t)$ of all extensions of tense $\mathsf{S4}$. It defines tense logics $\mathsf{S4BP}{n,m}^{k,l}$ with bounded width, depth and z-degree, gives characterizations of pretabular logics in several such extension lattices, and proves an anti-dichotomy theorem for the cardinality of pretabular extensions in $\mathsf{NExt}(\mathsf{S4}_t)$.

© 2026. Qian CHEN. All rights reserved.