Balbiani, Philippe, van der Hoek, Wiebe and Kuijer, Louwe B 
ORCID: 0000-0001-6696-9023
(2023)
Simple Axioms for Local Properties.
In: TARK-2023, Oxford, UK.
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Abstract
Correspondence theory allows us to create sound and complete axiomatizations for modal logic on frames with certain properties. For example, if we restrict ourselves to transitive frames we should add the axiom □ϕ → □□ϕ which, among other things, can be interpreted as positive introspection. One limitation of this technique is that the frame property and the axiom are assumed to hold globally, i.e., the relation is transitive throughout the frame, and the agent’s knowledge satisfies positive introspection in every world. In a modal logic with local properties, we can reason about properties that are not global. So, for example, transitivity might hold only in certain parts of the model and, as a result, the agent’s knowledge might satisfy positive introspection in some worlds but not in others. Van Ditmarsch et al. [9] introduced sound and complete axiomatizations for modal logics with certain local properties. Unfortunately, those axiomatizations are rather complex. Here, we introduce far simpler axiomatizations for a wide range of local properties.
| Item Type: | Conference or Workshop Item (Unspecified) |
|---|---|
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 15 May 2023 08:52 |
| Last Modified: | 20 Sep 2023 22:07 |
| DOI: | 10.4204/EPTCS.379.9 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3170259 |
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