Fernández-Duque, David; McLean, Brett; Zenger, Lukas (2023). A Family of Decidable Bi-intuitionistic Modal Logics. In: Marquis, Pierre; Son, Tran Cao; Kern-Isberner, Gabriele (eds.) 20th International Conference on Principles of Knowledge Representation and Reasoning. Rhodes, Greece. September 2-8, 2023. 10.24963/kr.2023/26
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We investigate intuitionistic logics extended with both the
co-implication connective of Hilbert–Brouwer logic and with
diamond and box modalities. We use a Kripke semantics based
on frames with two ‘forth’ confluence conditions on the modal
relation with respect to the intuitionistic relation. We give
sound and strongly complete axiomatisations for entailment
on this class of frames, and give similar axiomatisations for the
subclasses of frames satisfying any combination of reflexivity,
transitivity, and seriality. We then prove that all of these
logics are decidable, by proving that they have the finite frame
property.
Item Type: |
Conference or Workshop Item (Paper) |
|---|---|
Division/Institute: |
08 Faculty of Science > Institute of Computer Science (INF) > Logic and Theory Group (LTG) 08 Faculty of Science > Institute of Computer Science (INF) |
UniBE Contributor: |
Zenger, Lukas Matthias |
Subjects: |
000 Computer science, knowledge & systems 500 Science > 510 Mathematics |
ISSN: |
2334-1033 |
ISBN: |
978-1-956792-02-7 |
Language: |
English |
Submitter: |
Armand Singh Satjeevan Feuilleaubois |
Date Deposited: |
20 Mar 2024 12:20 |
Last Modified: |
20 Mar 2024 12:20 |
Publisher DOI: |
10.24963/kr.2023/26 |
Additional Information: |
Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning |
BORIS DOI: |
10.48350/194297 |
URI: |
https://boris.unibe.ch/id/eprint/194297 |
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