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Modal Hyperdoctrine: Higher-Order and Non-normal Extensions

  • 2024
  • OriginalPaper
  • Chapter
Published in:
Authors
Florrie Verity
Yoshihiro Maruyama
Published in
Logic, Language, Information, and Computation
Publisher
Springer Nature Switzerland

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Abstract

The chapter delves into the intricacies of modal hyperdoctrine semantics, extending traditional Kripke semantics to encompass quantified modal logics. It introduces a generalized presentation of modal hyperdoctrine for a many-sorted typed language and weaker base propositional modal logics, connecting these to intuitionistic hyperdoctrines via a translation theorem. The chapter further explores higher-order modal hyperdoctrines, proving their soundness and completeness, and concludes with future directions for research. This comprehensive approach offers a unified framework for studying various modal logics, making it a valuable resource for researchers in the field.
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previous chapter Completeness of Finitely Weighted Kleene Algebra with Tests
next chapter Validity in Contexts
Title
Modal Hyperdoctrine: Higher-Order and Non-normal Extensions
Authors
Florrie Verity
Yoshihiro Maruyama
Copyright Year
2024
Book
Logic, Language, Information, and Computation

Print ISBN: 978-3-031-62686-9

Electronic ISBN: 978-3-031-62687-6

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-62687-6_15
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