Marin, S;
Pereira, LC;
Pimentel, E;
Sales, E;
(2021)
A Pure View of Ecumenical Modalities.
In:
Logic, Language, Information, and Computation. WoLLIC 2021. Lecture Notes in Computer Science.
(pp. pp. 388-407).
Springer: Cham, Switzerland.
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Abstract
Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK, where exactly one logical operator figures in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK. We prove that nEK is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions.
| Type: | Proceedings paper |
|---|---|
| Title: | A Pure View of Ecumenical Modalities |
| Event: | WoLLIC 2021: Logic, Language, Information, and Computation |
| ISBN-13: | 978-3-030-88852-7 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-030-88853-4_24 |
| Publisher version: | https://doi.org/10.1007/978-3-030-88853-4_24 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10141795 |
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