Istituto di Scienza e Tecnologie dell'Informazione     
Straccia U., Ojeda-Aciego M., Viegas Damasio C. On fixed-points of multi-valued functions and their application to generalized logic programs. Technical report, 2007.
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.
Subject Fixed-Points
Multi-valued function
Logic Programming
F. Theory of Computation

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