Non-Rigid Designators in Modal and Temporal Free Description Logics (Extended Version)
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 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.
Cite
@article{arxiv.2405.07656,
title = {Non-Rigid Designators in Modal and Temporal Free Description Logics (Extended Version)},
author = {Alessandro Artale and Roman Kontchakov and Andrea Mazzullo and Frank Wolter},
journal= {arXiv preprint arXiv:2405.07656},
year = {2024}
}