Inference and Learning for Probabilistic Description Logics

The last years have seen an exponential increase in the interest for the development of methods for combining probability with Description Logics (DLs). These methods are very useful to model real world domains, where incompleteness and uncertainty are common. This combination has become a fundamental component of the Semantic Web. Our work started with the development of a probabilistic semantics for DL, called DISPONTE (”DIstribution Semantics for Probabilistic ONTologiEs“, Spanish for ”get ready“). DISPONTE applies the distribution semantics [Sato, 1995] to DLs. The distribution semantics is one of the most effective approaches in logic programming and is exploited by many languages, such as Independent Choice Logic, Probabilistic Horn Abduction, PRISM, pD, Logic Programs with Annotated Disjunctions, CP-logic, and ProbLog. Under DISPONTE we annotate axioms of a theory with a probability, that can be interpreted as an epistemic probability, i.e., as the degree of our belief in the corresponding axiom, and we assume that each axiom is independent of the others. DISPONTE, like the distribution semantics, defines a probability distribution over regular knowledge bases (also called worlds). To create a world, we decide whether to include or not each probabilistic axiom, then we multiply the probability of the choices done to compute the probability of the world. The probability of a query is then obtained from the joint probability of the worlds and the query by marginalization. Consider the Knowledge Base (KB) below: