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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
-
38
5
1881-1911
0097-5397
-
-
http://dx.doi.org/10.1137/070695976
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Umberto Straccia and Manuel Ojeda-Aciego and Carlos Viegas Damásio, On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs, SIAM Journal on Computing (SICOMP), Vol. 38, No. 5, Pag. 1881-1911, Society for Industrial and Applied Mathematics, ISBN 0097-5397, (http://dx.doi.org/10.1137/070695976), January 2009.
<b>Umberto Straccia, Manuel Ojeda-Aciego and <a href="/people/members/view.php?code=feecf7159d8e22c70a3bf33436444903" class="author">Carlos Viegas Damásio</a></b>, <u>On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs</u>, SIAM Journal on Computing (SICOMP), Vol. 38, No. 5, Pag. 1881-1911, Society for Industrial and Applied Mathematics, ISBN 0097-5397, (<a href="http://dx.doi.org/10.1137/070695976" target="_blank">url</a>), January 2009.
@article {StracciaAD09:siam, author = {Umberto Straccia and Manuel Ojeda-Aciego and Carlos Viegas Dam{\'a}sio}, title = {On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs}, journal = {SIAM Journal on Computing (SICOMP)}, publisher = {Society for Industrial and Applied Mathematics}, volume = {38}, number = {5}, pages = {1881-1911}, isbn = {0097-5397}, url = {http://dx.doi.org/10.1137/070695976}, 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.}, keywords = {fixed-points, multivalued functions, complete lattices, logic programming}, month = {January}, year = {2009}, }
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