Reasoning for ALCQ extended with a flexible meta-modelling hierarchy

TL;DR

This paper introduces ALCQM, an extension of Description Logic ALCQ with a flexible meta-modelling hierarchy, enabling integration of ontologies through meta-relationships, and provides a tableau algorithm for consistency checking.

Contribution

It extends ALCQ with meta-modelling capabilities by adding statements that relate individuals to concepts, allowing multi-level meta-relationships, and proves a correctness tableau algorithm.

Findings

Defined ALCQM with meta-modelling hierarchy

Developed a tableau algorithm for consistency checking

Proved the correctness of the algorithm

Abstract

This works is motivated by a real-world case study where it is necessary to integrate and relate existing ontologies through meta- modelling. For this, we introduce the Description Logic ALCQM which is obtained from ALCQ by adding statements that equate individuals to concepts in a knowledge base. In this new extension, a concept can be an individual of another concept (called meta-concept) which themselves can be individuals of yet another concept (called meta meta-concept) and so on. We define a tableau algorithm for checking consistency of an ontology in ALCQM and prove its correctness.