Non-Normal Modal Description Logics (Extended Version)
Tiziano Dalmonte, Andrea Mazzullo, Ana Ozaki, Nicolas Troquard

TL;DR
This paper introduces a family of non-normal modal description logics with neighbourhood semantics, providing tableau-based algorithms for satisfiability checking and analyzing their computational complexity.
Contribution
It extends ALC-based description logics with non-normal modal operators and develops modular tableau algorithms with complexity analysis for these systems.
Findings
Developed tableau-based satisfiability algorithms for non-normal modal description logics.
Provided complexity results: NExpTime for general systems, ExpTime for certain fragments.
Reduced some systems to satisfiability on relational models.
Abstract
Modal logics are widely used in multi-agent systems to reason about actions, abilities, norms, or epistemic states. Combined with description logic languages, they are also a powerful tool to formalise modal aspects of ontology-based reasoning over an object domain. However, the standard relational semantics for modalities is known to validate principles deemed problematic in agency, deontic, or epistemic applications. To overcome these difficulties, weaker systems of so-called non-normal modal logics, equipped with neighbourhood semantics that generalise the relational one, have been investigated both at the propositional and at the description logic level. We present here a family of non-normal modal description logics, obtained by extending ALC-based languages with non-normal modal operators. For formulas interpreted on neighbourhood models over varying domains, we provide a modular…
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Semantic Web and Ontologies · Multi-Agent Systems and Negotiation
