Concept learning in the description logic ALCH(D) based onminimal model reasoning for RDF data

In this paper, we propose an algorithm for ALCH(D) concept learning from RDF data using minimal model reasoning. This algorithm generates concept expressions in the Description Logic ALCH(D) by giving background knowledge and positive and negative examples in the RDF form. Our method can be widely applied to RDF data on the Web, as background knowledge. An advantage of the method for RDF data is that reasoning on RDF graphs is tractable compared to logical reasoning for OWL data. We solve the problem that RDF data cannot be directly applied to the concept learning due to its less expressive power, specifically, the lack of negative expressions. In order to construct expressive ALCH(D) concepts from less expressive RDF data in the concept learning, we introduce (nonmonotonic inference rules based on minimal model reasoning which derive implicit subclass and subproperty relations from the background knowledge in the RDF form. We prove the soundness, completeness and decidability of the nonmonotonic RDF reasoning in the minimal Herbrand models for RDF graphs. The process of concept learning is divided in two parts: (i) concept generation and (ii) concept evaluation. In the concept generation, minimal model reasoning enables us to derive complex concepts consisting of negation, conjunction, disjunction and quantifiers and to exclude inconsistent concepts. In the concept evaluation, we evaluate hypothesis concepts with class and property hierarchies where minimal model reasoning is used for expressing more specific concepts as the answer for learning. We implement a system that learns some ALCH(D) concepts describing the features of given examples.