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Hennessy-Milner Properties for (Modal) Bi-intuitionistic Logic

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Logic, Language, Information, and Computation (WoLLIC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11541))

Abstract

Bi-intuitionistic logic is an extension of intuitionistic propositional logic with a binary operator that is residuated with respect to disjunction. Our main result is a Hennessy-Milner property for bi-intuitionistic logic interpreted over certain classes of Kripke models. We generalise this to obtain a corresponding result for modal bi-intuitionistic logic. Our main technical tools are a categorical duality between (modal) descriptive Kripke frames and (modal) bi-Heyting algebras, and the use of behavioural equivalence.

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Authors and Affiliations

  1. The Australian National University, Canberra, Australia

    Jim de Groot & Dirk Pattinson

Authors
  1. Jim de Groot
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  2. Dirk Pattinson
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Correspondence to Jim de Groot or Dirk Pattinson .

Editor information

Editors and Affiliations

  1. Department of Philosophy and Religious Studies, Utrecht University, Utrecht, The Netherlands

    Rosalie Iemhoff

  2. Utrecht Institute of Linguistics OTS, Utrecht University, Utrecht, The Netherlands

    Michael Moortgat

  3. Centro de Informática, Universidade Federal de Pernambuco (UFPE), Recife, Brazil

    Ruy de Queiroz

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de Groot, J., Pattinson, D. (2019). Hennessy-Milner Properties for (Modal) Bi-intuitionistic Logic. In: Iemhoff, R., Moortgat, M., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2019. Lecture Notes in Computer Science(), vol 11541. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59533-6_10

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  • DOI: https://doi.org/10.1007/978-3-662-59533-6_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-59532-9

  • Online ISBN: 978-3-662-59533-6

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