Decomposing Ordinal Sums in Neural Multi-adjoint Logic Programs

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, G¨odel 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, G¨odel and Łukasiewicz conjunctors.

• Type: Conference
• Year: 2004
• Where: IBERAMIA
• Authors: Jesús Medina, Enrique Mérida Casermeiro, Manuel Ojeda-Aciego
• Keywords: Artificial Intelligence, IBERAMIA 2004, Multi-adjoint Logic, Multi-adjoint Logic Programs, Ordinal Sum