On reductants in the framework of multi-adjoint logic programming

Reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties. As it has been reported, when interpreted on a partially ordered structure, a multi-adjoint logic program has to include all its reductants in order to preserve the approximate completeness property. After a short survey of the different notions of reductant that have been developed for multi-adjoint logic programs, we introduce a new and more adequate notion of reductant in the multi-adjoint framework. We study some of its properties and its relationships with other notions of reductants, and provide an algorithm for computing all the reductants associated with a multi-adjoint logic program.