Affiliation:
1. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, 1983969411, Iran
Abstract
Abstract
In this paper, we consider the logic ${\textsf{ITL}}^{e}$, a variant of intuitionistic linear temporal logic that is interpreted over the class of dynamic Kripke frames. These are bi-relational structures of the form $ \langle{W, \preccurlyeq , f}\rangle $ where $\preccurlyeq $ is a partial order on $W$ and $f: W \to W$ is a $\preccurlyeq $-monotone function. Our main result answers a question recently raised by Boudou et al. (2017, A decidable intuitionistic temporal logic. In Computer Science Logic 2017, pp. 14:1–14:17. Vol. 82 of LIPIcs) about axiomatizing this logic. We provide an axiomatization of ${\textsf{ITL}}^{e}$ and prove its strong completeness with respect to the class of all dynamic Kripke frames. The proposed axiomatization is infinitary; it has two derivation rules with countably many premises and one conclusion. It should be mentioned that ${\textsf{ITL}}^{e}$ is semantically non-compact, so no finitary proof system for this logic could be strongly complete.
Publisher
Oxford University Press (OUP)
Subject
Logic,Hardware and Architecture,Arts and Humanities (miscellaneous),Software,Theoretical Computer Science
Reference26 articles.
1. Variations in access control logic;Abadi,2008
2. Bisimulations for intuitionistic temporal logics;Balbiani,2018
3. Intuitionistic linear temporal logics;Balbiani;ACM Transactions on Computational Logic,2020
4. Temporal here and there;Balbiani,2016
5. Fibred security language;Boella;Studia Logica,2009
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