Decomposing Ordinal Sums in Neural Multi-Adjoint Logic Programs

Abstract. The theory of multi-adjoint logic programs has been introduced as a unifying framework to deal with uncertainty, imprecise data or incomplete information. From the applicative part, a neural net based implementation of homogeneous propositional multi-adjoint logic programming on the unit interval has been presented elsewhere, but restricted to the case in which the only connectives involved in the program were the usual product, Gödel and Łukasiewicz together with weighted sums. A modification of the neural implementation is presented here in order to deal with a more general family of adjoint pairs, including conjunctors constructed as an ordinal sum of a finite family of basic conjunctors. This enhancement greatly expands the scope of the initial approach, since every t-norm (the type of conjunctor generally used in applications) can be expressed as an ordinal sum of product, Gödel and Łukasiewicz conjunctors.