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Non-Rigid Designators in Modal and Temporal Free Description Logics (Extended Version) (2405.07656v2)

Published 13 May 2024 in cs.LO

Abstract: Definite descriptions, such as 'the General Chair of KR 2024', are a semantically transparent device for object identification in knowledge representation. In first-order modal logic, definite descriptions have been widely investigated for their non-rigidity, which allows them to designate different objects (or none at all) at different states. We propose expressive modal description logics with non-rigid definite descriptions and names, and investigate decidability and complexity of the satisfaction problem. We first systematically link satisfiability for the one-variable fragment of first-order modal logic with counting to our modal description logics. Then, we prove a promising NEXPTIME-completeness result for concept satisfiability for the fundamental epistemic multi-agent logic $\mathbf{S5}{n}$ and its neighbours, and show that some expressive logics that are undecidable with constant domain become decidable (but Ackermann-hard) with expanding domains. Finally, we conduct a fine-grained analysis of decidability of temporal logics.

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Authors (4)
  1. Alessandro Artale (15 papers)
  2. Roman Kontchakov (15 papers)
  3. Andrea Mazzullo (11 papers)
  4. Frank Wolter (42 papers)
Citations (1)
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