Programación lógica multiadjunta no monótona y ecuaciones bipolares de relaciones difusasextensiones y relaciones

Résumé

A novel non-monotonic logic programming framework has been presented, adapting the philosophy of the multi-adjoint paradigm to normal logic programs and defining a proper stable model semantics. Additionally, sufficient conditions for the existence and uniqueness of stable models have been provided. Including a strong negation in this generalized framework, we have chosen the most suitable notion of coherence, and we have provided different measures for the incoherence of a multi-adjoint normal logic program. Afterwards, a generalized version of multi-adjoint normal logic programs, called extended multi-adjoint logic programming, has been presented, in which a special kind of rules, called constraints, have been included and in which operators with multiple order-reversing arguments are allowed to appear in the body of the rules. These programs have then been transformed into the simplest logic programming structure which preserves its semantics. Besides, we show how the existence and unicity conditions of stable models for multi-adjoint logic programs could be applied in other different logic programming approaches. A complete study on the resolution of bipolar multi-adjoint fuzzy relation equations on symmetric multi-adjoint birresiduated lattices has been developed. In particular, this study generalizes the existing results in the literature about bipolar fuzzy relation equations. Furthermore, the special case of bipolar fuzzy relation equations defined with the product t-norm and its adjoint negation has been analysed. Namely, this negation is a non-involutive negation. Finally, an original procedure to solve an abduction problem in multi-adjoint normal logic programming by means of bipolar multi-adjoint fuzzy relation equations has been described.