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A logic program consists of a set of Horn clauses, and can be used to express a query on relational data bases. It is shown that logic programs express precisely the queries in YE⁺ (the set of queries representable by a fixpoint applied to a positive existential query). Queries expressible by logic programs are thus not first-order queries in general, nor are all the first-order queries expressible as logic programs. Several ways of adding negation to logic programs are examined. The most general case is where arbitrary first-order formulas (with “nonterminal” relation symbols) are allowed. The resulting class has the expressive power of universally quantified second-order logic.