Axiomatizability of Alexandrov Dynamic Topological Logic

Dynamical systems provide rigorous models of movement or evolution over time. Due to their abstract nature, they may be naturally employed for representing e.g. physical, biological, or financial phenomena. Specifically in the context of Computer Science, computational processes, machine learning algorithms, and multi-agent systems may be regarded as dynamical systems. This has sparked interest in designing formal specification languages for dynamical systems which could potentially be employed for automated or computer-assisted deduction, leading to the introduction of dynamic topological logic (DTL). When space is continuous but time is discrete, it is known that a sound and complete deductive calculus for DTL exists. However, discrete spaces are not uncommon in CS applications , and in this setting, whether such a calculus exists even in principle has been an open question for more than two decades. More precisely, it was unknown whether the DTL of Alexandrov spaces is computably enumerable. In this paper, we use model search techniques to provide an affirmative answer.