On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs

Authors:
Umberto Straccia;Manuel Ojeda-Aciego;Carlos V. Damásio
Affiliations:
straccia@isti.cnr.it;aciego@uma.es;cd@di.fct.unl.pt
Venue:
SIAM Journal on Computing
Year:
2009

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Abstract

Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. First, we overview and investigate the existence and computation of minimal fixed-points of multivalued 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 multivalued operator can be defined whose fixed-points are in one-to-one correspondence with the models of the logic program.