Complete Intuitionistic Temporal Logics in Topological Dynamics
Joseph Boudou, Mart\'in Di\'eguez, David Fern\'andez-Duque

TL;DR
This paper axiomatizes and proves completeness for intuitionistic temporal logic over topological dynamics, extending the understanding of its decidability and applicability to various spaces.
Contribution
It provides a formal axiomatization and completeness results for intuitionistic temporal logic in topological dynamics, including specific fragments and spaces.
Findings
Decidability of the logic established by Fernández-Duque
Axiomatization of the logic and its fragments provided
Completeness proven for several familiar topological spaces
Abstract
The language of linear temporal logic can be interpreted over the class of dynamic topological systems, giving rise to the intuitionistic temporal logic , recently shown to be decidable by Fern\'andez-Duque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.
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