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Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents

Authors Tim Lyon , Alwen Tiu, Rajeev Goré, Ranald Clouston

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LIPIcs.CSL.2020.28.pdf
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ACM Subject Classification
  • Theory of computation → Proof theory
  • Theory of computation → Automated reasoning
Keywords
  • Bi-intuitionistic logic
  • Interpolation
  • Nested calculi
  • Proof theory
  • Sequents
  • Tense logics

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Abstract

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants.

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Tim Lyon, Alwen Tiu, Rajeev Goré, and Ranald Clouston. Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CSL.2020.28

Author Details

Tim Lyon
  • Institut für Logic and Computation, Technische Universität Wien, Austria
Alwen Tiu
  • Research School of Computer Science, The Australian National University, Australia
Rajeev Goré
  • Research School of Computer Science, The Australian National University, Australia
Ranald Clouston
  • Research School of Computer Science, The Australian National University, Australia

Funding

  • Lyon, Tim: Supported by the European Union Horizon 2020 Marie Skłodowska-Curie grant No 689176 and FWF projects I 2982, Y544-N2, and W1255-N23.

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