Duality for Goal-Driven Query Processing in Disjunctive Deductive Databases

Abstract

Bottom-up query-answering procedures tend to explore a much larger search space than what is strictly needed. Top-down processing methods use the query to perform a more focused search that can result in more efficient query answering. Given a disjunctive deductive database, i>DB, and a query, i>Q, we establish a strong connection between model generation and clause derivability in two different representations of i>DB and i>Q. This allows us to use a bottom-up procedure for evaluating i>Q against i>DB in a top-down fashion. The approach requires no extensive rewriting of the input theory and introduces no new predicates. Rather, it is based on a certain i>duality principle for interpreting logical connectives. The duality transformation is achieved by reversing the direction of implication arrows in the clauses representing both the theory and the negation of the query. The application of a generic bottom-up procedure to the transformed clause set results in top-down query answering. Under favorable conditions efficiency gains are substantial, as shown by our preliminary testing. We give the logical meaning of the duality transformation and point to the conditions and sources of improved efficiency. We show how the duality approach can be used for i>refined query answering by specifying the i>minimal conditions (weakest updates) to i>DB under which i>Q becomes derivable. This is shown to be useful for view updates in disjunctive deductive databases as well as for other interesting applications.