The adjoint method was first developed for aerodynamic shape optimization applications through the use of control theory by Jameson (1998) in the late 1980s and early 1990s, using ideas adapted from more general work by Lions (1971) on optimal control of systems governed by partial differential equations (PDEs). Over the past two decades, adjoint methods have been used in a variety of applicati...

This paper presents a formulation for the obtainment of the sensitivity analysis of a point wise error estimator with respect to the nodal coordinates using the adjoint state method. The proposed point wise error estimator is based on the SPR method. The numerical accuracy of the presented sensitivity analysis has been tested by perturbing a mesh. The capability of the presented sensitivity ana...

Multi-adjoint logic programs has been recently introduced [9, 10] as a generalization of monotonic logic programs [2, 3], in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. This paper discusses abductive reasoning—that is, reasoning in which explanatory hypotheses are formed and evaluated. To model uncertainty in human cogniti...

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...