Towards Distributed Tableaux Reasoning Procedure for DDL with Increased Subsumption Propagation between Remote Ontologies

Distributed Description Logics (DDL) enable reasoning with multiple ontologies interconnected by direc- tional semantic mapping. In DDL semantic mapping is indicated by so called bridge rules. There are two kinds: into- and onto-bridge rules. Mappings between concepts allow subsumption to propagate from one ontology to another. However, in some cases, espe- cially when more than two local ontologies are involved, subsumption does not always propagate as we would expect. In a recent study, an adjusted se- mantics has been introduced that is able to cope with more complex scenarios. In particular, subsumption propagates along chains of several bridge rules under this new semantics. This study makes use of so called compositional consistency requirement that has been employed before in Package-based description logics. While the results concerning subsumption propaga- tion under the adjusted semantics are encouraging, we show in this paper that this semantics also has drawbacks. In certain situations it violates the di- rectionality principle. We propose a weaker version of the semantics in this paper that is able to cope with chains of onto-bridge rules but it is not able to deal with chains of into-bridge rules. Furthermore we provide a sound and complete tableaux reasoning algorithm for this semantics