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From Display to Labelled Proofs for Tense Logics

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10703)

Abstract

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic \(\textsf {Kt}\), the image is shown to be the set of all proofs in the labelled calculus \(\textsf {G3Kt}\).

Keywords

  • Display calculus
  • Labelled calculus
  • Structural proof theory
  • Tense logic
  • Modal logic

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Notes

  1. 1.

    More specifically, this is true of a display calculus for a logic such that every structural connective can be interpreted as a connective of the logic.

  2. 2.

    Extending to primitive tense axioms [14] is straightforward though more syntactically involved.

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Acknowledgments

Work supported by the FWF projects: START Y544-N23 and I 2982.

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Correspondence to Tim Lyon .

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Ciabattoni, A., Lyon, T., Ramanayake, R. (2018). From Display to Labelled Proofs for Tense Logics. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2018. Lecture Notes in Computer Science(), vol 10703. Springer, Cham. https://doi.org/10.1007/978-3-319-72056-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-72056-2_8

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