On updates of hybrid knowledge bases composed of ontologies and rules

Throughout the last decade, two distinct knowledge representation paradigms have been standardised to capture rich metadata on the Web: ontology languages based on Classical Logic and reasoning rules based on Logic Programming. Both offer important features for knowledge representation and the interest in their integration has recently resulted in frameworks for hybrid knowledge bases that consist of an ontology and a rule component. Instead of the usual static view of hybrid knowledge, in this paper we address its dynamics and in particular focus on updates. We develop two hybrid update semantics that fit the needs of particular use cases of hybrid knowledge and provide the expected results when used in specific application domains. The first semantics uses a given ontology update operator to update the ontology component of a hybrid knowledge base in the presence of static rules. Inspired by a realistic application, and based on a generalised notion of splitting, known from Logic Programming, the second semantics offers a way to modularly combine an ontology update operator with a rule update semantics. It can be used for performing updates of hybrid knowledge bases consisting of ontology and rule layers that share information through a rule-based interface. Both of these developments constitute solutions to the problem of hybrid updates for restricted classes of hybrid knowledge bases. We examine their fundamental formal properties and show that despite the different ideas behind each of them, they are fully compatible with one another, i.e. when both are applicable, they lead to the same result.