Tableau Algorithms for E-Connections of Description Logics

For many years, the Modal Logic community has pursued various techniques for robustly combining logics. These methodologies reflect a new direction in Logic applied to Knowledge Representation, namely the direction toward constructing and investigating complex combined logical formalisms out of simpler ones. The E-Connections framework is a novel technique for combining Abstract Description Systems (ADSs), a generalization of several families of decidable logics, including Description Logics, Modal Logics, as well as many logics of time and space. In this paper, we investigate different E-Connection languages involving Description Logics. Recently, E-Connections of Description Logics have been proposed as a suitable formalism for various applications, such as ontology integration on the Semantic Web. We propose two novel combinations: one-way E-Connections and E-Connections allowing for transitive and symmetric link relations. Then, we investigate in depth the problem of reasoning with E-Connections and provide different tableau-based decision procedures. Finally, we show that our algorithms can be implemented as an extension of existing DL reasoners and present our prototype implementation in the Pellet system. To the best of our knowledge, the algorithms presented in this paper are the first practical decision procedures for E-Connections.