An ExpTime Upper Bound for $\mathcal{ALC}$ with Integers (Extended Version) Article Swipe

MAKE IMPACT

Nadia Labai , Magdalena Ortiz , Mantas Šimkus · YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2006.02078

Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual DLs while keeping the complexity of reasoning in check. For expressive DLs and in the presence of general TBoxes, for standard reasoning tasks like consistency, the most general decidability results are for the so-called $ω$-admissible domains, which are required to be dense. Supporting non-dense domains for features that range over integers or natural numbers remained largely open, despite often being singled out as a highly desirable extension. The decidability of some extensions of $\mathcal{ALC}$ with non-dense domains has been shown, but existing results rely on powerful machinery that does not allow to infer any elementary bounds on the complexity of the problem. In this paper, we study an extension of $\mathcal{ALC}$ with a rich integer domain that allows for comparisons (between features, and between features and constants coded in unary), and prove that consistency can be solved using automata-theoretic techniques in single exponential time, and thus has no higher worst-case complexity than standard $\mathcal{ALC}$. Our upper bounds apply to some extensions of DLs with concrete domains known from the literature, support general TBoxes, and allow for comparing values along paths of ordinary (not necessarily functional) roles.

Type

preprint

Language

en

Landing Page

http://arxiv.org/abs/2006.02078

PDF

https://arxiv.org/pdf/2006.02078

OA Status

green

References

24

Related Works

20

OpenAlex ID

https://openalex.org/W3033862888

Raw OpenAlex JSON

OpenAlex ID

https://openalex.org/W3033862888

Canonical identifier for this work in OpenAlex

DOI

https://doi.org/10.48550/arxiv.2006.02078

Digital Object Identifier

Title

An ExpTime Upper Bound for $\mathcal{ALC}$ with Integers (Extended Version)

Work title

Type

preprint

OpenAlex work type

Language

en

Primary language

Publication year

2020

Year of publication

Publication date

2020-06-03

Full publication date if available

Authors

Nadia Labai, Magdalena Ortiz, Mantas Šimkus

List of authors in order

Landing page

https://arxiv.org/abs/2006.02078

Publisher landing page

PDF URL

https://arxiv.org/pdf/2006.02078

Direct link to full text PDF

Open access

Yes

Whether a free full text is available

OA status

green

Open access status per OpenAlex

OA URL

https://arxiv.org/pdf/2006.02078

Direct OA link when available

Concepts

Unary operation, Decidability, Extension (predicate logic), Consistency (knowledge bases), Domain (mathematical analysis), Integer (computer science), Discrete mathematics, Upper and lower bounds, EXPTIME, Computer science, Omega, Description logic, Succinctness, Binary number, Range (aeronautics), Mathematics, Computational complexity theory, Theoretical computer science, Algorithm, Arithmetic, Physics, PSPACE, Quantum mechanics, Programming language, Materials science, Mathematical analysis, Composite material

Top concepts (fields/topics) attached by OpenAlex

Cited by

0

Total citation count in OpenAlex

References (count)

24

Number of works referenced by this work

Related works (count)

20

Other works algorithmically related by OpenAlex

Full payload