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Coalgebraic Geometric Logic

Authors Nick Bezhanishvili, Jim de Groot , Yde Venema

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Author Details

Nick Bezhanishvili
  • Institute of Logic, Language and Computation, University of Amsterdam, The Netherlands
Jim de Groot
  • Department of Engineering and Computer Science, The Australian National University, Canberra, Australia
Yde Venema
  • Institute of Logic, Language and Computation, University of Amsterdam, The Netherlands

Acknowledgements

The authors want to express their gratitude to the anonymous referees for many constructive and helpful comments.

Cite AsGet BibTex

Nick Bezhanishvili, Jim de Groot, and Yde Venema. Coalgebraic Geometric Logic. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.CALCO.2019.7

Abstract

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor T on some full subcategory of the category Top of topological spaces and continuous functions. We compare the notions of modal equivalence, behavioural equivalence and bisimulation on the resulting class of models, and we provide a final object for the corresponding category. Furthermore, we specify a method of lifting an endofunctor on Set, accompanied by a collection of predicate liftings, to an endofunctor on the category of topological spaces.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
Keywords
  • Coalgebra
  • Geometric Logic
  • Modal Logic
  • Topology

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Related Versions

  • A report version of the paper is available at https://arxiv.org/abs/1903.08837. The presented material originates from the master’s thesis of the second author, supervised by the first and third author.

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