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Comonadic semantics for hybrid logic

Authors Samson Abramsky , Dan Marsden

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Samson Abramsky
  • University College London, London, UK
Dan Marsden
  • University of Oxford, Oxford, UK

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Samson Abramsky and Dan Marsden. Comonadic semantics for hybrid logic. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.MFCS.2022.7

Abstract

Hybrid logic is a widely-studied extension of basic modal logic, which corresponds to the bounded fragment of first-order logic. We study it from two novel perspectives: (1) We apply the recently introduced paradigm of comonadic semantics, which provides a new set of tools drawing on ideas from categorical semantics which can be applied to finite model theory, descriptive complexity and combinatorics. (2) We give a novel semantic characterization of hybrid logic in terms of invariance under disjoint extensions, a minimal form of locality. A notable feature of this result is that we give a uniform proof, valid for both the finite and infinite cases.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
Keywords
  • comonads
  • model comparison games
  • semantic characterizations
  • hybrid logic
  • bounded fragment

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