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On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs
January 2009
StracciaAD09:siam
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.
Journal
Umberto Straccia, Manuel Ojeda-Aciego, Carlos Viegas Damásio
SIAM Journal on Computing (SICOMP)
Society for Industrial and Applied Mathematics
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38
5
1881-1911
0097-5397
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http://dx.doi.org/10.1137/070695976
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