Marin, Sonia;
Carlos Pereira, Luiz;
Pimentel, Elaine;
Sales, Emerson;
(2025)
Separability and harmony in ecumenical systems.
Journal of Logic and Computation
, 35
(6)
, Article exae058. 10.1093/logcom/exae058.
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Abstract
The quest of smoothly combining logics so that connectives from different logics can co-exist in peace has been a fascinating topic of research. In 2015, Dag Prawitz introduced a natural deduction system for an ecumenical first-order logic, unifying classical and intuitionistic logics within a shared language. Building upon this foundation, we introduced, in a series of works, sequent systems for ecumenical logics and modal extensions. In this work we propose a new pure sequent calculus version for Prawitz’s original system, where each rule features precisely one logical operator. This is achieved by extending sequents with an additional context, called stoup, and establishing the ecumenical concept of polarities. We smoothly extend these ideas for handling modalities, presenting a new pure labelled system for ecumenical modal logics. Finally, we show how this allows for naturally retrieving the ecumenical modal nested system proposed in a previous work.
| Type: | Article |
|---|---|
| Title: | Separability and harmony in ecumenical systems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/logcom/exae058 |
| Publisher version: | https://doi.org/10.1093/logcom/exae058 |
| Language: | English |
| Additional information: | © The Author(s) 2025. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Ecumenical systems, modalities, nested systems, labelled systems, cut-elimination, polarities. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10216309 |
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