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This paper investigates the problem of approximating conjunctive queries without self-joins on probabilistic databases by lower and upper bounds that can be computed more efficiently. We study this problem via an indirection: Given a propositional formula &phis;, find formulas in a more restricted language that are greatest lower bound and least upper bound, respectively, of &phis;. We study bounds in the languages of read-once formulas, where every variable occurs at most once, and of read-once formulas in disjunctive normal form. We show equivalences of syntactic and model-theoretic characterisations of optimal bounds for unate formulas, and present algorithms that can enumerate them with polynomial delay. Such bounds can be computed by queries expressed using first-order queries extended with transitive closure and a special choice construct. Besides probabilistic databases, these results can also benefit the problem of approximate query evaluation in relational databases, since the bounds expressed by queries can be computed in polynomial combined complexity.

On the optimal approximation of queries using tractable propositional languages