Implicational Completeness of Signed Resolution

deduction. The main reason for this is probably the conception that implicational completeness, in contrast to refutational completeness, is of no practical significance. Moreover, it fails for all important refinements of Robinson's original resolution calculus. In addition, Lee's proof [7] is presented in an unsatisfactory manner (to say the least). A fourth reason for the widespread neglect of implicational completeness might be the fact that Lee (and others at that time) did not distinguish between implication and subsumption of clauses. However, nowadays, it is well known that the first relation between clauses is undecidable [10], whereas sophisticated and efficient algorithms for testing the latter one are at the core of virtually all successful resolution theorem provers (see, e.g., [4]). With hindsight, this is decisive for the significance of Lee's Theorem. We will provide a new and independent proof of implicational complete