On generalized Horn formulas and k-resolution

Abstract A hierarchy of classes H k of propositional formulas has been introduced by Yamasaki and Doshita (1983) and Gallo and Scutella (1988) . The classes H k have polynomially solvable satisfiability problem, and the basic class is the set of Horn formulas. We show that the k -resolution is complete and sound for H k , where k -resolution is a restriction of ordinary resolution, in that at least one of the parent clauses has at most k literals. Furthermore, we discuss to what extent the class of unsatisfiable formulas in H k and the class of unsatisfiable formulas for which a k -resolution refutation exists coincide.