Concept constructing in the description logic SROIQ based on minimal RDF reasoning

In the area of the Semantic Web, the expressive description logic SROIQ corresponding to OWL2 provides us rich reasoning and learning tasks for ontologies, e.g., inference engine, query-answering system, and concept learning. However, unlike simple ontologies in RDF graphs, it is not easy for users to build ontologies using the logical and complex expressions of SROIQ. In this paper, we propose (i) minimal model reasoning in the description logic SROIQ for RDF graphs and (ii) a SROIQ-concept constructing algorithm for the classes, properties and individuals in each RDF graph. In the minimal models of RDF graphs based on the closed world assumption (CWA), we prove the completeness, soundness and complexity of the minimal model r0065asoning in the description logic SROIQ. We define decidable SROIQ-concept constructing in a unique interpretation of SROIQ-conc&pts based on the mini-mal model reasoning. For infinite SROIQ-concept combinations constructed by classes, properties and individuals (even less expressive description logic concepts), our const|ructing method removes semantically identifying concepts, e.g., An A, AnAnA,…if concept name A exists, in the minimal models. As a main theoretical result, we show the decidability and complexity of the concept constructing algorithm. We formalize two applications to the concept constructing algorithm as a SROIQ-concept query system and SROIQ-concepl learning for RDF graphs. The query system for RDF graphs returns the answers of expressive SROIQ queries including concept variables. The concept learning enables us to logically induce SROIQ-concepts from positive and negative examples in knowledge bases. © 2020, Japanese Society for Artificial Intelligence. All rights reserved.