  Classical algorithms for query optimization presuppose the absence of
inconsistencies or uncertainties in the database and exploit only valid
semantic knowledge provided, e.g., by integrity constraints. Data inconsistency
or uncertainty, however, is a widespread critical issue in ordinary databases:
total integrity is often, in fact, an unrealistic assumption and violations to
integrity constraints may be introduced in several ways.
  In this report we present an approach for semantic query optimization that,
differently from the traditional ones, relies on not necessarily valid semantic
knowledge, e.g., provided by violated or soft integrity constraints, or induced
by applying data mining techniques. Query optimization that leverages invalid
semantic knowledge cannot guarantee the semantic equivalence between the
original user's query and its rewriting: thus a query optimized by our approach
yields approximate answers that can be provided to the users whenever fast but
possibly partial responses are required. Also, we evaluate the impact of use of
invalid semantic knowledge in the rewriting of a query by computing a measure
of the quality of the answer returned to the user, and we rely on the recent
theory of Belief Logic Programming to deal with the presence of possible
correlation in the semantic knowledge used in the rewriting.
