Non-Rigid Designators in Modal and Temporal Free Description Logics

Artale, A. and Kontchakov, Roman and Mazzullo, A. and Wolter, F. (2024) Non-Rigid Designators in Modal and Temporal Free Description Logics. In: Marquis, P. and Ortiz, M. and Pagnucco, M. (eds.) Proceedings of the 21st International Conference on Principles of Knowledge Representation and Reasoning. IJCAI, pp. 82-93. ISBN 9781956792058.

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 satisfiability 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 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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• Non-Rigid Designators in Modal and Temporal Free Description Logics. (deposited 17 Dec 2024 14:06) [Currently Displayed]

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