Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)

TL;DR

This paper introduces a novel approach for updating hybrid knowledge bases that combine ontologies and nonmonotonic rules, addressing the challenge of knowledge evolution in dynamic open worlds.

Contribution

It proposes the first update operator for hybrid knowledge bases, extending existing work on ABox updates with rules and providing a formal semantics.

Findings

Extended ABox updates with rules

Proposed a semantics for evolving hybrid knowledge bases

Analyzed properties of the update operator

Abstract

The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.