Proving implications by algebraic approximation

This paper applies techniques of algebraic approximation to provide effective algorithms to determine the validity of universally quantified implications over lattice structures. We generalize the known result which states that any semilattice is approximated in the two element lattice. We show that the validity of a universally quantified implication ψ over a possibly infinite domain can be determined by examining its validity over a simpler domain the size of which is related to the number of constants in ψ. Both the known as well as the new results have high potential in providing practical automated techniques in various areas of application in computer science.