Query Languages for Constraint Databases: First-Order Logic, Fixed-Points, and Convex Hulls
We define various extensions of first-order logic on linear as well as polynomial constraint databases. First, we extend first-order logic by a convex closure operator and show this logic, FO(conv), to be closed and to have Ptime data-complexity. We also show that a weak form of multiplication is definable in this language and prove the equivalence between this language and the multiplication part of PFOL. We then extend FO(conv) by fixed-point operators to get a query languages expressive enough to capture Ptime. In the last part of the paper we lift the results to polynomial constraint databases.
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