Implicational Completeness of Signed Resolution

Abstract

Every serious computer scientist and logician knows that resolution is complete for first-order clause logic. By this, of course, one means that the empty clause (representing contradiction) is derivable by resolution from every unsatisfiable set of clauses S. However, there is another — less well known — concept of completeness for clause logic, that is often referred to as “Lee’s Theorem” (see, e.g., [8]): Char-tung Lee’s dissertation [7] focused on an interesting observation that (in a corrected version and more adequate terminology) can be stated as follows: Theorem 1 (Lee). Let S be a set of clauses. For every non-tautological clause C that is logically implied by S there is clause D, derivable by resolution from S, such that D subsumes C.