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Equational theories and database constraints

We present a novel way to formulate database dependencies as sentences of first-order logic, using equational statements instead of Horn clauses. Dependency implication is directly reduced to equational implication. Our approach is powerful enough to express functional and inclusion dependencies, which are the most common database constraints. We present a new proof procedure for these dependencies. We use our equational formulation to derive new upper and lower bounds for the complexity of their implication problems.