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With the fast development of Semantic Web, more and more RDF and OWL ontologies are created and shared. The effective management, such as storage, inference and query, of these ontologies on databases gains increasing attention. This paper addresses ontology query answering on databases by means of Datalog programs. Via epistemic operators, integrity constraints are introduced, and used for conveying semantic aspects of OWL that are not covered by Datalog-style rule languages. We believe such a processing suitable to capture ontologies in the database flavor, while keeping reasoning tractable. Here, we present a logically equivalent knowledge base whose (sound and complete) inference system appears as a Datalog program. As such, SPARQL query answering on OWL ontologies could be solved in databases. Bi-directional strategies, taking advantage of both forward and backward chaining, are then studied to support this kind of customized Datalog programs, returning exactly answers to the query within our logical framework.