Eckhardt, Timo;
Pym, David J;
(2024)
Base-extension semantics for modal logic.
Logic Journal of the IGPL
, Article jzae004. 10.1093/jigpal/jzae004.
(In press).
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Abstract
In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT, K4 and S4, with as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between and a natural presentation of ♦. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases.
| Type: | Article |
|---|---|
| Title: | Base-extension semantics for modal logic |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/jigpal/jzae004 |
| Publisher version: | https://doi.org/10.1093/jigpal/jzae004 |
| Language: | English |
| Additional information: | Copyright © The Author(s) 2024. 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: | Modal logic, proof-theoretic semantics, base-extension semantics |
| 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/10186240 |
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