An Algebraic View on p-Admissible Concrete Domains for Lightweight Description Logics

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Contributors

Abstract

Concrete domains have been introduced in Description Logics (DLs) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. To retain decidability when integrating a concrete domain into a decidable DL, the domain must satisfy quite strong restrictions. In previous work, we have analyzed the most prominent such condition, called ω -admissibility, from an algebraic point of view. This provided us with useful algebraic tools for proving ω -admissibility, which allowed us to find new examples for concrete domains whose integration leaves the prototypical expressive DL ALC decidable. When integrating concrete domains into lightweight DLs of the EL family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. In the present paper, we investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Although ω -admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into ALC yields decidable DLs.

Details

Original languageEnglish
Title of host publicationLogics in Artificial Intelligence - 17th European Conference, JELIA 2021, Proceedings
EditorsWolfgang Faber, Gerhard Friedrich, Martin Gebser, Michael Morak
Place of PublicationCham
PublisherSpringer International Publishing
Pages194-209
Number of pages16
Volume12678
ISBN (electronic)978-3-030-75775-5
ISBN (print)978-3-030-75774-8
Publication statusPublished - 2021
Peer-reviewedYes

Publication series

SeriesLecture Notes in Computer Science, Volume 12678
Volume12678
ISSN0302-9743

External IDs

Scopus 85111143571
ORCID /0000-0002-4049-221X/work/142247980

Keywords

Keywords

  • Admissibility, Concrete domains, Constraint satisfaction, Convexity, Decidability, Description logic, Finite boundedness, p-admissibility, Tractability

Library keywords