Effective Query Answering with Ontologies and DBoxes

Abstract

The goal of this chapter is to survey the formalisation of a precise and uniform integration between first-order ontologies, first-order queries, and classical relational databases (DBoxes) We include here non-standard variants of first-order logic, such as the one with active domain semantics and standard name assumption, used typically in database theory. We present a general framework for the rewriting of a domain independent first-order query in presence of an arbitrary domain independent first-order logic ontology over a signature extending a database signature with additional predicates. The framework supports deciding the existence of a logically equivalent and – given the ontology – safe-range first-order reformulation (called exact reformulation) of a domain independent first-order query in terms of the database signature, and if such a reformulation exists, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (i.e., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. We finally present an application of the framework with the very expressive \(\mathcal {ALCHOI}\) and \(\mathcal {SHOQ}\) description logics ontologies, by providing effective means to compute safe-range first-order exact reformulations of queries.