The Precise Complexity of Reasoning in ALC with ω-Admissible Concrete Domains (Extended Version)

Stefan BorgwardtStefan Borgwardt, Filippo De BortoliFilippo De Bortoli, Patrick KoopmannPatrick Koopmann

Stefan Borgwardt, Filippo De Bortoli, Patrick Koopmann
The Precise Complexity of Reasoning in ALC with ω-Admissible Concrete Domains (Extended Version)
Technical Report, arXiv.org, volume CoRR abs/2405.19096, May 2024

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KurzfassungAbstract
Concrete domains have been introduced in the context of Description Logics to allow references to qualitative and quantitative values. In particular, the class of ω-admissible concrete domains, which includes Allen's interval algebra, the region connection calculus (RCC8), and the rational numbers with ordering and equality, has been shown to yield extensions of ALC for which concept satisfiability w.r.t. a general TBox is decidable. In this paper, we present an algorithm based on type elimination and use it to show that deciding the consistency of an ALC(𝔇) ontology is ExpTime-complete if the concrete domain 𝔇 is ω-admissible and its constraint satisfaction problem is decidable in exponential time. While this allows us to reason with concept and role assertions, we also investigate feature assertions f(a,c) that can specify a constant c as the value of a feature f for an individual a. We show that, under conditions satisfied by all known ω-admissible domains, we can add feature assertions without affecting the complexity.
Weitere Informationen unter:Further Information: Link
Projekt:Project: CPEC, ScaDS.AI
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@misc{BoBoKo-DL-24-arxiv,
      title={The Precise Complexity of Reasoning in $\mathcal{ALC}$ with $\omega$-Admissible Concrete Domains (Extended Version)}, 
      author={Stefan {Borgwardt} and Filippo {De Bortoli} and Patrick {Koopmann}},
      year={2024},
      eprint={2405.19096},
      archivePrefix={arXiv},
      primaryClass={cs.LO},
      url={https://arxiv.org/abs/2405.19096}, 
}