We study a general framework for query rewriting in the presence of an arbitrary first-order logic ontology over a database signature. The framework supports deciding the existence of a safe-range first-order equivalent reformulation of a query in terms of the database signature, and if so, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (e.g., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. At the end, we present a non-trivial application of the framework with ontologies in the very expressive ALCHOIQ description logic, by providing effective means to compute safe-range first-order exact reformulations of queries.

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A schema mapping is a high-level specification in which the relationship between two database schemas is described. In data exchange, schema mappings are one-way mappings that describe which data can be brought from source data to target data. Therefore, given a source instance and a mapping, there might be more than one valid target instance. This fact causes many problems in query answering over target data for non-conjunctive queries. To make query answering feasible for all queries, we focus on a methodology for extending the original schema mapping to guarantee the uniqueness of target instance corresponding to a source instance. To this end, we introduce a theoretical framework where the problem is transformed to an abduction problem, namely, definability abduction. We apply the framework to relational data exchange setting and solve the problem by pointing out minimal solutions according to a specific semantic minimality criterion.

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