On Fixed-points of Multi-valued Functions on Complete Lattices and their Application to Generalized Logic Programs .

In SIAM Journal on Computing, 200x.

Abstract:
Unlike monotone single-valued functions, multi-valued mappings may have none, one or (possibly infinitely) many minimal fixed-points.

The contribution of this work is twofold. At first 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. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice. We show that a multi-valued operator can be defined whose fixed-points are in one-to-one correspondence with the models of the logic program.