On fixed-points of multi-valued functions and their application to generalized logic programs

Unlike monotone single-valued functions, multi-valued mappings may have none, one or (possibly infinitely) many minimal fixed-points. In this work we overview and investigate about the existence and computation of minimal fixed-points of multi-valued mappings, whose domain is a complete lattice and whose range is its power set. We then show how these results are applied to a very general form of (monotone) logic programs, where the truth space is a complete lattice. We show that multi-valued operators can be defined whose fixed-points are in one-to-one correspondence with the models of the logic program.