KR2025Proceedings of the 22nd International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 22nd International Conference on Principles of Knowledge Representation and Reasoning

Melbourne, Australia. November 11-17, 2025.

Edited by
  1. Magdalena Ortiz
  2. Renata Wassermann
  3. Torsten Schaub

ISSN: 2334-1033
ISBN: 978-1-956792-08-9

Sponsored by
Published by

Copyright © 2025 International Joint Conferences on Artificial Intelligence Organization

Expressive Description Logics with Rich Yet Affordable Numeric Constraints

  1. Federica Di Stefano(Institute of Logic and Computation, TU Wien)
  2. Sanja Lukumbuzya(Institute of Logic and Computation, TU Wien)
  3. Magdalena Ortiz(Institute of Logic and Computation, TU Wien)
  4. Mantas Šimkus(Institute of Logic and Computation, TU Wien)
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BibTeX
https://doi.org/10.24963/kr.2025/66

Keywords

  1. Description Logics
  2. Numeric Constraints
  3. Computational Complexity
  4. Integer Programming
  5. Optimization

Abstract

Description Logics (DLs) excel at representing structured knowledge in several application domains, but fall very short when it comes to reasoning about their numeric aspects. We consider the expressive DL ALCHOIQ with closed predicates and extend it with features ranging over user-specified finite numeric intervals, feature assertions, and local additive constraints on feature values. We illustrate the power of this language for describing problems that involve ontological and numeric reasoning and study reasoning problems that go beyond satisfiability, such as finding models that minimize some costs. We show that these additional numeric modeling and reasoning capabilities can be accommodated by extending a standard reasoning technique for ALCHOIQ using linear inequalities, and the extension does not necessarily increase the worst-case computational cost.