Inference in Probabilistic Ontologies with Attributive Concept Descriptions and Nominals

This paper proposes a probabilistic description logic that combines (i) constructs of the well-known ALC logic, (ii) probabilistic assertions, and (iii) limited use of nominals. We start with our recently proposed logic crALC, where any ontology can be translated into a relational Bayesian network with partially specified probabilities. We then add nominals to restrictions, while keeping crALC’s interpretation-based semantics. We discuss the clash between a domain-based semantics for nominals and an interpretation-based semantics for queries, keeping the latter semantics throughout. We show how inference can be conducted in crALC and present examples with real ontologies that display the level of scalability of our proposals.