Generalized resolution for 0-1 linear inequalities

We show how the resolution method of theorem proving can be extended to obtain a procedure for solving a fundamental problem of integer programming, that of finding all valid cuts of a set of linear inequalities in 0-1 variables. Resolution generalizes to two cutting plane operations that, when applied repeatedly, generate all strongest possible or "prime " cuts (analogous to prime implications in logic). Every valid cut is then dominated by at least one of the prime cuts. The algorithm is practical when restricted to classes of inequalities within which one can easily tell when one inequality dominates another. We specialize the algorithm to several such classes, including inequalities representing logical clauses, for which it reduces to classical resolution