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.