Numeric reasoning in the Semantic Web

The Semantic Web is an effort by the W3C to enable integration and sharing of information across different applications and organizations using annotations by means of ontology instances. With the growth of such data, two important problems need to be addressed: (1) a scalability issue and (2) a performance issue for reasoning. Main memory reasoners are efficient for reasoning, but they hardly support real size data. This paper discusses the use of databases, more precisely of ontology-based databases (OBDBs), for managing Semantic Web annotation data. Such systems are able to manage real-size data. But the main weakness of databases are their poor deductive reasoning capabilities. Thus, we propose an approach that consists in enriching annotation instances with new numeric-valued or string-valued properties allowing to replace deductive reasoning by numeric queries. We define formally some cases where this approach may be implemented and we propose extension of ontology languages allowing to represent explicitly their structures. Ontology being recorded in OBDB, these extensions allow the OBDB system to perform dynamically the instance enrichment and to rewrite queries as numeric queries. This approach is in particular used for geometric reasoning, and we present its implementation within OntoDB, an OBDB developed in our laboratory.