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Dedekind-MacNeille completion and Cartesian product of multi-adjoint lattices. (English) Zbl 1269.06003

Summary: Fuzzy logic programming tries to introduce fuzzy logic into logic programming in order to provide new-generation computer languages which incorporate comfortable programming resources for helping the development of applications where uncertainty could play an important role. In this sense, the mathematical concept of multi-adjoint lattice has been successfully exploited into the so-called multi-adjoint logic programming approach, MALP in brief, for modelling flexible notions of truth-degrees beyond the simpler case of true and false. In this paper, we focus on two relevant mathematical concepts for this kind of domains useful for evaluating MALP. On the one side, we adapt the classical notion of Dedekind-MacNeille completion in order to relax some usual hypothesis on such kind of ordered sets, and next we study the advantages of generating multi-adjoint lattices as the Cartesian product of previous ones. On the practical side, we show that the formal mechanisms described before have direct correspondences with interesting debugging tasks in the Fuzzy Logic Programming Environment for Research, FLOPER in brief, developed in our research group.

MSC:

06B23 Complete lattices, completions
68N17 Logic programming

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