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Recapturing Dynamic Logic of Relation Changers via Bounded Morphisms

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Abstract

The present contribution shows that a Hilbert-style axiomatization for dynamic logic of relation changers is complete for the standard Kripke semantics not by a well-known rewriting technique but by the idea of an auxiliary semantics studied by van Benthem and Wang et al. A key insight of our auxiliary semantics for dynamic logic of relation changers can be described as: “relation changers are bounded morphisms.” Moreover, we demonstrate that this semantic insight can be used to provide a modular cut-free labelled sequent calculus for the logic in the sense that our calculus can be regarded as a natural expansion of a labelled sequent calculus of iteration-free propositional dynamic logic.

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Acknowledgements

We would like to thank Johan van Benthem for his helpful and detailed comments to our draft. We also would like to thank Yanjing Wang for his comments and suggestions on a possible direction of further study at AWPL 2018. We would like to acknowledge anonymous reviewers for their helpful comments and suggestions on our manuscript. We are very grateful to editors and staff of Studia Logica for their kind and continuous supports. Both authors were partially supported by JSPS Core-to-Core Program (A. Advanced Research Networks). The work of the second author was also partially supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (C) Grant Number 19K12113 and JSPS KAKENHI Grant-in-Aid for Scientific Research (B) Grant Number 17H02258.

Funding Funding was provided by Japan Society for the Promotion of Science (Core-to-Core Program A. Advanced Research Networks), Japan Society for the Promotion of Science (Grant No. 19K12113), and Japan Society for the Promotion of Science (Grant No. 17H02258).

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Authors and Affiliations

  1. Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, Japan

    Ryo Hatano

  2. Faculty of Humanities and Human Sciences, Hokkaido University, Nishi 7 Chome, Kita 10 Jo, Kita-ku, Sapporo, Hokkaido, Japan

    Katsuhiko Sano

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  1. Ryo Hatano
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  2. Katsuhiko Sano
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Correspondence to Ryo Hatano.

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Hatano, R., Sano, K. Recapturing Dynamic Logic of Relation Changers via Bounded Morphisms. Stud Logica 109, 95–124 (2021). https://doi.org/10.1007/s11225-020-09902-5

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