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Two-Dimensional Kripke Semantics I: Presheaves

Author G. A. Kavvos

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Author Details

G. A. Kavvos
  • University of Bristol, United Kingdom

Funding

This work was supported by the UKRI Engineering and Physical Sciences Research Council grants EP/Y000242/1, EP/Y033418/1, the UKRI International Science Partnerships Fund (ISPF), and a Royal Society Research Grant.

Acknowledgements

I have benefitted significantly from conversations with Dan Licata, Nachiappan Valliappan, Fabian Ruch, Amar Hadzihasanovic, Kohei Kishida, Sean Moss, Sam Staton, Daniel Gratzer, Lars Birkedal, Jonathan Sterling, Philip Saville, and Gordon Plotkin.

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G. A. Kavvos. Two-Dimensional Kripke Semantics I: Presheaves. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FSCD.2024.14

Abstract

The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely through their categorical semantics. We show how the two correspond.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Categorical semantics
Keywords
  • modal logic
  • categorical semantics
  • Kripke semantics
  • duality
  • open maps

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