@inproceedings{e5429789655944dc8682984a4bf11533,
title = "Syntactic interpolation for tense logics and bi-intuitionistic logic via nested sequents",
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.",
keywords = "Bi-intuitionistic logic, Interpolation, Nested calculi, Proof theory, Sequents, Tense logics",
author = "Tim Lyon and Alwen Tiu and Rajeev Gor{\'e} and Ranald Clouston",
note = "Publisher Copyright: {\textcopyright} Tim Lyon, Alwen Tiu, Rajeev Gor{\'e}, and Ranald Clouston.; 28th EACSL Annual Conference on Computer Science Logic, CSL 2020 ; Conference date: 13-01-2020 Through 16-01-2020",
year = "2020",
month = jan,
doi = "10.4230/LIPIcs.CSL.2020.28",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Maribel Fernandez and Anca Muscholl",
booktitle = "28th EACSL Annual Conference on Computer Science Logic, CSL 2020",
address = "Germany",
}