The Precise Complexity of Reasoning in $\mathcal{ALC}$ with $ω$-Admissible Concrete Domains

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

$The Precise Complexity of Reasoning in $\mathcal{ALC}$ with $ω$-Admissible Concrete Domains$

ISSN: 1613-0073

Stefan Borgwardt, Filippo De Bortoli, Patrick Koopmann
The Precise Complexity of Reasoning in $\mathcal{ALC}$ with $ω$-Admissible Concrete Domains
In Laura Giordano, Jean Christoph Jung, Ana Ozaki, eds., Proceedings of the 37th International Workshop on Description Logics (DL'24), volume 3739 of CEUR Workshop Proceedings, June 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 $\omega$-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 $\mathcal{ALC}$ 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 $\mathcal{ALC}(\mathfrak{D})$ ontology is ExpTime-complete if the concrete domain $\mathfrak{D}$ is $\omega$-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 $\omega$-admissible domains, we can add feature assertions without affecting the complexity.
Bemerkung: Note: An extended version of this paper can be found at: https://arxiv.org/abs/2405.19096
Weitere Informationen unter:Further Information: Link
Projekt:Project: ScaDS.AI
Forschungsgruppe:Research Group: AutomatentheorieAutomata Theory

@inproceedings{ BaBoKo-DL-24,
      address = {Bergen, Norway},
      author = {Stefan {Borgwardt} and Filippo {De Bortoli} and Patrick {Koopmann}},
      booktitle = {Proceedings of the 37th International Workshop on Description Logics (DL'24) },
      editor = {Laura {Giordano} and Jean Christoph {Jung} and Ana {Ozaki}},
      publisher = {CEUR-WS},
      series = {{CEUR} Workshop Proceedings},
      title = {{The Precise Complexity of Reasoning in $\mathcal{ALC}$ with $\omega$-Admissible Concrete Domains}},
      volume = {3739},
      year = {2024},
    }