Ontology-Based Probabilistic Reasoning
Description Logics (DLs) constitute a family of knowledge representation formalisms that has been successfully employed in various application domains. The particular syntax of a DL allows one to form axioms, which in turn, are used to encode the knowledge of a particular domain. Intuitively, a DL ontology is a (finite) set of such axioms, which restricts the possible set of interpretations over a knowledge domain.
The motivation behind this dissertation is the fact that classical DL ontologies are not suited to represent contextual knowledge inherent to many real world applications. Our goal is to investigate context-based reasoning techniques to close this gap. In a nutshell, we view each context as a subset of the given ontology. Given the possibility to distinguish a piece of knowledge relatıve to the context it is entailed from leads to different non-standard reasoning problems in DL ontologies, which constitutes the basis in this thesis.
We employ context-based reasoning to facilitate probabilistic reasoning over DL ontologies by defining a probability distribution over the context space with the help of a Bayesian Network. The resulting formalism, Bayesian DLs, is a family of probabilistic DLs where every piece of knowledge is associated with a (conditional) probability: Every consequence of the ontology is a probabilistic consequence, determined accordıng the probabilities of the contexts it is entailed from. Several reasoning problems have been studied in this setting, leading to tight complexity bounds for some Bayesian DLs.