Non-Rigid Designators in Modal and Temporal Free Description Logics (Extended Version)
<|reference_start|>Non-Rigid Designators in Modal and Temporal Free Description Logics (Extended Version): 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.<|reference_end|>
@article{artale2024non-rigid,
    title={Non-Rigid Designators in Modal and Temporal Free Description Logics
  (Extended Version)},
    author={Alessandro Artale, Roman Kontchakov, Andrea Mazzullo, Frank Wolter},
    journal={arXiv preprint arXiv:2405.07656},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.07656},
    primaryClass={cs.LO}
}