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DOI: 10.4230/LIPIcs.CSL.2020.28

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

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

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

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)

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@InProceedings{lyon_et_al:LIPIcs.CSL.2020.28,
  author =	{Lyon, Tim and Tiu, Alwen and Gor\'{e}, Rajeev and Clouston, Ranald},
  title =	{{Syntactic Interpolation for Tense Logics and Bi-Intuitionistic Logic via Nested Sequents}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.28},
  URN =		{urn:nbn:de:0030-drops-116713},
  doi =		{10.4230/LIPIcs.CSL.2020.28},
  annote =	{Keywords: Bi-intuitionistic logic, Interpolation, Nested calculi, Proof theory, Sequents, Tense logics}
}

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

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