Zakharyaschev, Michael and Alekseev, A. (1995) All finitely axiomatizable normal extensions of K4.3 are decidable. Mathematical Logic Quarterly 41 (1), pp. 15-23. ISSN 0942-5616.
Abstract
We use the apparatus of the canonical formulas introduced by Zakharyaschev [10] to prove that all finitely axiomatizable normal modal logics containing K4.3 are decidable, though possibly not characterized by classes of finite frames. Our method is purely frame-theoretic. Roughly, given a normal logic L above K4.3, we enumerate effectively a class of (possibly infinite) frames with respect to which L is complete, show how to check effectively whether a frame in the class validates a given formula, and then apply a Harropstyle argument to establish the decidability of L, provided of course that it has finitely many axioms.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hall |
| Date Deposited: | 08 Nov 2021 19:41 |
| Last Modified: | 09 Aug 2023 12:52 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/46656 |
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