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

TL;DR

This paper introduces expressive modal description logics with non-rigid definite descriptions, analyzing their decidability and complexity, especially in multi-agent epistemic and temporal contexts, revealing new decidability results.

Contribution

It systematically links satisfiability in first-order modal logic with counting to modal description logics and explores decidability and complexity in multi-agent and temporal logics.

Findings

NEXPTIME-completeness for concept satisfiability in $ extbf{S5}^n$

Decidability of some expressive logics with expanding domains

Fine-grained analysis of temporal logic decidability

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.