Relationships Between Probabilistic Description and First-Order Logics

This paper analyzes the probabilistic description logic P-SHIQ as a fragment of first-order probabilistic logic (FOPL). P-SHIQ was suggested as a language that is capable of representing and reasoning about different kinds of uncertainty in ontologies, namely generic probabilistic relationships between concepts and probabilistic facts about individuals. However, some semantic properties of P-SHIQ have been unclear which raised concerns regarding whether it could be used for representing probabilistic ontologies. In this paper we provide an insight into its semantics by translating P-SHIQ into FOPL with a specific semantics based on possible worlds. From that reduction, we show that some of the restrictions of P-SHIQ are fundamental and sketch alternative semantic foundations for a probabilistic description logic.