Reasoning in Non-normal Modal Description Logics

TL;DR

This paper introduces tableau algorithms for reasoning in non-normal modal description logics, extending ALC with non-normal modal operators, and analyzes their satisfiability and complexity in various semantic settings.

Contribution

It develops terminating, correct, and complete tableau algorithms for non-normal modal description logics and explores their satisfiability complexity in different model restrictions.

Findings

Tableau algorithms for non-normal modal description logics are correct and complete.

Satisfiability problems are analyzed with tight complexity bounds.

Restrictions to constant domain models simplify reasoning complexity.

Abstract

Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary results on reasoning in a family of modal description logics obtained by combining ALC with non-normal modal operators. First, we provide a framework of terminating, correct, and complete tableau algorithms to check satisfiability of formulas in such logics with the semantics based on varying domains. We then investigate the satisfiability problems in fragments of these languages obtained by restricting the application of modal operators to formulas only, and interpreted on models with constant domains, providing tight complexity results.