Paper: Axiomatizability of Alexandrov Dynamic Topological Logic (at LICS 2026)

Authors: Niels C. Vooijs David Fernández-Duque

Open access: https://doi.org/10.4230/LIPIcs.LICS.2026.81

Abstract

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.

BibTeX

  @InProceedings{VooijsFernandezDuqu-AxiomatizabilityofA,
    author = 	 {Niels C. Vooijs and David Fernández-Duque},
    title = 	 {Axiomatizability of Alexandrov Dynamic Topological Logic},
    booktitle =  {Proceedings of the Forty-First Annual Symposium on Logic in Computer Science (LICS 2026)},
    year =	 {2026},
    month =	 {July}, 
    pages =      {81:1--81:26},
    location =   {Lisbon, Portugal}, 
    publisher =	 {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
    doi =        {10.4230/LIPIcs.LICS.2026.81}
  }