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DOI: 10.4230/LIPIcs.FSCD.2026.20

Relational Dualities and Bisimulation

Authors: Piotr Kozicki and G. A. Kavvos

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract

The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational systems (e.g. the states of a machine), the corresponding algebra is one of logical predicates on these systems (e.g. predicates on these states, i.e. program logics). Our aim is to extend this phenomenon to relations, putting well-behaved relations between systems (e.g. bisimulations) in correspondence with relations between predicates. This is achieved by constructing particular relational extensions of Tarski duality (for infinitary classical propositional logic) and Thomason duality (for infinitary classical modal logic). We sketch how these dualities give rise to a proof system that relates formulae between different systems.

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Piotr Kozicki and G. A. Kavvos. Relational Dualities and Bisimulation. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kozicki_et_al:LIPIcs.FSCD.2026.20,
  author =	{Kozicki, Piotr and Kavvos, G. A.},
  title =	{{Relational Dualities and Bisimulation}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.20},
  URN =		{urn:nbn:de:0030-drops-263703},
  doi =		{10.4230/LIPIcs.FSCD.2026.20},
  annote =	{Keywords: bisimulation, modal logic, duality, categorical semantics}
}

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Relational Dualities and Bisimulation

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