Among other applications, multi-adjoint lattices have been successfully used for modeling flexible notions of truth-degrees in the fuzzy extension of logic programming called MALP (Multi-Adjoint Logic Programming). In this paper we focus in the completion of such mathematical construct by adapting the classical notion of Dedekind-MacNeille in order to relax this usual hypothesis on such kind of...

Multi-adjoint logic program generalise monotonic logic programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, a procedural semantics is given for the paradigm of multiadjoint logic programming and completeness theorems are proved.

We present a neural net based implementation of propositional [0, 1]-valued multiadjoint logic programming. The implementation needs some preprocessing of the initial program to transform it in a homogeneous program; then, transformation rules carry programs into neural networks, where truth-values of rules relate to output of neurons, truth-values of facts represent input, and network function...

The framework of multi-adjoint logic programming has shown to cover a number of approaches to reason under uncertainty, imprecise data or incomplete information. In previous works, we have presented a neural implementation of its fix-point semantics for a signature in which conjunctors are built as an ordinal sum of a finite family of basic conjunctors (Gödel and Lukasiewicz t-norms). Taking in...

The hypotheses required for the quasicompleteness theorems [5, 7] are restated in terms of termination properties of a calculation algorithm.

Multi-adjoint logic programs were recently proposed as a generalization of monotonic and residuated logic programs, in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, the need of biresiduated pairs is justified through the study of a very intuitive family of operators, which turn out to be not necessarily commuta...

This paper presents an adjoint method for the optimum shape design of unsteady flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the non-linear frequency domain method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the non-linear frequency domain adjoint e...

Algorithmic Differentiation (AD) provides the analytic derivatives of functions given as programs. Adjoint AD, which computes gradients, is similar to Back Propagation for Machine Learning. AD researchers study strategies to overcome the difficulties of adjoint AD, to get closer to its theoretical efficiency. To promote fruitful exchanges between Back Propagation and adjoint AD, we present thre...

The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the n-dimensional radial momentum operator is not self-adjoint and has no selfadjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on L[(0,∞), dr] which is n...

The focus of CFD applications has shifted to aerodynamic design. This shift has been mainly motivated by the availability of high performance computing platforms and by the development of new and efficient analysis and design algorithms. In particular automatic design procedures, which use CFD combined with gradient-based optimization techniques, have had a significant impact on the design proc...