---
title: "Bounded Predicates in Description Logics with Counting"
authors:
  - "Sanja Lukumbuzya"
  - "Mantas Simkus"
doi: "10.24963/ijcai.2021/271"
url: "https://ijcai.org/proceedings/2021/271"
pdf: "https://ijcai.org/proceedings/2021/0271.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "1966-1972"
track: "Main Track"
keywords:
  - "Knowledge Representation and Reasoning: Logics for Knowledge Representation"
  - "Knowledge Representation and Reasoning: Description Logics and Ontologies"
---

# Bounded Predicates in Description Logics with Counting

Sanja Lukumbuzya, Mantas Simkus

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 1966-1972. DOI: [10.24963/ijcai.2021/271](https://doi.org/10.24963/ijcai.2021/271)

## Abstract

Description Logics (DLs) support so-called anonymous objects, which significantly contribute to the expressiveness of these KR languages, but also cause substantial computational challenges. This paper investigates reasoning about upper bounds on predicate sizes for ontologies written in the expressive
DL ALCHOIQ extended with closed predicates. We describe a procedure based on integer programming that allows us to decide the existence of upper bounds on the cardinality of some predicate in the models of a given ontology in a data-independent way. Our results yield a promising supporting tool for constructing higher quality ontologies, and provide a new way to push the decidability frontiers. To wit, we define a new safety condition for Datalog-based
queries over DL ontologies, while retaining decidability of query entailment.