Generalized Bottom-Up Query Evaluation

Our goal is to generalize the well known bottom-up, set-oriented query evaluation for deductive databases in two aspects: First, we consider arbitrary clauses as rules in the database, not only Horn clauses or clauses with stratified negation. This allows to represent disjunctive information, in the database as well as in answers to queries. We utilize NF2 relations for modelling sets of disjunctive facts and operations of the corresponding relational algebra for computing consequences and answers. Thus our algorithm should be of practical importance for applying database techniques in generalized deductions. Second, we parameterize the implicit database completion which underlies query evaluation. The classical rule for Horn clause databases, which only assumes the negation of facts not implied by the database, is not applicable to disjunctive databases. Moreover, the choice of completion often depends on the intended application. Therefore we allow the specification of arbitrary clauses as defaults, and we extend our algorithm to consider such general defaults.