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KR2023Proceedings of the 20th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 2-8, 2023.

Edited by
  1. Pierre Marquis,
  2. Tran Cao Son
  3. Gabriele Kern-Isberner

ISSN: 2334-1033
ISBN: 978-1-956792-02-7

Sponsored by
Published by

Copyright © 2023 International Joint Conferences on Artificial Intelligence Organization

A Family of Decidable Bi-intuitionistic Modal Logics

  1. David Fernández-Duque(University of Barcelona)
  2. Brett McLean(Ghent University)
  3. Lukas Zenger(University of Bern)
PDF
BibTeX
https://doi.org/10.24963/kr.2023/26

Keywords

  1. Uncertainty, vagueness, many-valued and fuzzy logics
  2. Computational aspects of knowledge representation
  3. Dealing with uncertain, incomplete or contradictory information
  4. Reasoning about knowledge, beliefs, and other mental attitudes

Abstract

We investigate intuitionistic logics extended both with 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.