Solving numerical constraints

In \cite{BockmayrWeispfenning01}, we give an overview of solving numerical constraints in the context of automated reasoning. Emphasis is on logical aspects of numerical constraints. We view them as atomic formulae in first-order predicate logic that are interpreted over some numerical domain like the real, rational, or integer numbers. We present various inference systems for reasoning with numerical constraints, describe the algebraic and geometric structure of their solution set, and present fundamental algorithms for deciding satisfiability, computing one or all solutions, and deducing new constraints