Leme, R;
Olarte, C;
Pimentel, E;
Coniglio, ME;
(2025)
The Modal Cube Revisited: Semantics Without Worlds.
In:
Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2025.
(pp. pp. 181-200).
Springer, Cham
![[thumbnail of main.pdf]](https://discovery.ucl.ac.uk/style/images/fileicons/text.png) |
Text
main.pdf - Published Version Access restricted to UCL open access staff until 26 September 2026. Download (551kB) |
Abstract
We present a non-deterministic semantic framework for all modal logics in the modal cube, extending prior works by Kearns and others. Our approach introduces modular and uniform multi-valued non-deterministic matrices (Nmatrices) for each logic, where necessitation is captured by the systematic use of level valuations. The semantics is grounded in an eight-valued system and provides a sound and complete decision procedure for each modal logic, extending and refining earlier semantics as particular cases. Additionally, we propose a novel model-theoretic perspective that links our framework to relational (Kripke-style) semantics, addressing longstanding questions regarding the correspondence between modal axioms and semantic conditions in non-deterministic settings. This yields a philosophically robust and technically modular alternative to traditional possible-world semantics.
| Type: | Proceedings paper |
|---|---|
| Title: | The Modal Cube Revisited: Semantics Without Worlds |
| Event: | Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2025 |
| ISBN-13: | 9783032060846 |
| DOI: | 10.1007/978-3-032-06085-3_10 |
| Publisher version: | https://doi.org/10.1007/978-3-032-06085-3_10 |
| 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 > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10216307 |
Archive Staff Only
 |
View Item |
