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Machine-Checked Proof-Theory for Propositional Modal Logics

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Advances in Proof Theory

Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 28))

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Abstract

We describe how we machine-checked the admissibility of the standard structural rules of weakening, contraction and cut for multiset-based sequent calculi for the unimodal logics S4, S4.3 and K4De, as well as for the bimodal logic \(\mathrm {S4C}\) recently investigated by Mints. Our proofs for both S4 and S4.3 appear to be new while our proof for \(\mathrm {S4C}\) is different from that originally presented by Mints, and appears to avoid the complications he encountered. The paper is intended to be an overview of how to machine-check proof theory for readers with a good understanding of proof theory.

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Notes

  1. 1.

    Technically, there are two syntactically identical premises which individually un-box one of the two copies of \(\Box A\).

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Acknowledgments

Jeremy E. Dawson—Supported by Australian Research Council Grant DP120101244.

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Authors and Affiliations

  1. Logic and Computation Group, School of Computer Science, The Australian National University, Canberra, ACT, 2601, Australia

    Jeremy E. Dawson, Rajeev Goré & Jesse Wu

Authors
  1. Jeremy E. Dawson
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  2. Rajeev Goré
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  3. Jesse Wu
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Corresponding author

Correspondence to Rajeev Goré .

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Editors and Affiliations

  1. Campus de Caparica DM FCT, Univ Nova de Lisboa, Caparica, Portugal

    Reinhard Kahle

  2. Inst.of Computer Sci. applied math., University of Bern, Bern, Switzerland

    Thomas Strahm

  3. Institute of Computer Science and A, University of Berne, Berne, Switzerland

    Thomas Studer

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Dawson, J.E., Goré, R., Wu, J. (2016). Machine-Checked Proof-Theory for Propositional Modal Logics. In: Kahle, R., Strahm, T., Studer, T. (eds) Advances in Proof Theory. Progress in Computer Science and Applied Logic, vol 28. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-29198-7_5

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