Continuous First-Order Constraint Satisfactionwith Equality and Disequality Constraints

In an earlier paper we have shown, how one can successfully use constraint satisfaction techniques for proving and solving formulae in the first-order predicate language over the reals (i.e., real first-order constraints). This approach was restricted to inputs that contain inequality symbols such as ≤, but no equality symbols (=) or disequality symbols ( 6=). In this paper we lay the basis for extending this approach to inputs that contain (dis)equalities. This considerably widens the applicability of constraint programming in areas such as control engineering, and builds a strong bridge to areas such as quantifier elimination, automated theorem proving, and computer algebra.