Reasoning Theory for D3L with Compositional Bridge Rules

The semantic mapping in Distributed Dynamic Description Logics(D3L) allows knowledge to propagate from one ontology to another. The current research for knowledge propagation in D3L is only for a simplified case when only two ontologies are involved. In this paper we study knowledge propagation in more complex cases. We find in the case when more than two ontologies are involved and bridge rules form chains, knowledge does not always propagate along chains of bridge rules even if we would expect it. Inspired by Package-based description Logics, we extend the original semantics of D3L by imposing so called compositional consistency condition on domain relations in D3L interpretations. Under this semantics knowledge propagates along chains of bridge rules correctly. Furthermore we provide a distributed Tableaux reasoning algorithm for deciding satisfiability of concepts which is decidable in D3L under compositional consistency. Compared with original one, the extended D3L provides more reasonable logic foundation for distributed, dynamic system such as the information integration system and the Semantic Web.