Notes on Ginsberg's multivalued logics

The use of multivalued logics for knowledge representation and nonmonotonic reasoning has often been advocated, in particular within the general framework proposed by Ginsberg in his paper "Multivalued logics: a uniform approach to reasoning in artificial intelligence." His system is based on a multivalued logic with an arbitrary number of truth values classified with respect to two partial orders, a truth order and a knowledge order. This classification is very interesting and gives an intuitive appeal to the framework. In this paper the work by Ginsberg is critically reviewed, pointing out some flaws and ways to overcome them. Moreover, we present some ideas on how to modify the original schema in order to obtain a more semantically well-founded framework.
L'utilisation de la Iogique multivalente pour la représentation des connaissances et le raisonnement non monotone a souvent été préconisée, en particulier à l'intérieur du cadre général proposé par Ginsberg dans son article intitulé〘 Multivalued logics: a uniform approach to reasoning in artificial intelligence 〙 Son système est basé sur une logique multivalente comportant un nombre arbitraire de valeurs de vérité classées selon deux ordres partiels: un ordre de vérité et un ordre de connaissances. Cette classification est très intéressante et donne un attrait intuitif au cadre. Dans cet article, l'auteur examine le travail de Ginsberg, y relève des lacunes et propose des moyens de les corriger. De plus, il expose certaines idées en vue de modifier le schéma original et ainsi obtenir un meilleur cadre du point de vue de la sémantique.     

Existence, uniqueness and stability of the equilibrium points of a SHARON bioreactor model

This paper addresses the dynamics of a SHARON reactor, a promising technology for ammonium removal from concentrated wastewater streams. The contraction mapping theorem is used to determine which operating conditions of a SHARON reactor with pH-control result in a unique equilibrium state. However, this approach only identifies the case of very large dilution rates, in practice corresponding with complete biomass wash-out, i.e. with complete loss of biological activity. Practical operation of a SHARON reactor aims at reaching ammonium conversion to nitrite. To identify such interesting operating points, the equilibrium points are subsequently calculated directly in terms of input variables for a simplified SHARON reactor model. The stability of the obtained equilibrium points is assessed and the corresponding phase portraits are analyzed. The influence of slightly varying parameter and input values is investigated as well.     

A constructive approach to sequential Nash equilibria

We present a Coq-formalized proof that all non-cooperative, sequential games have a Nash equilibrium point. Our proof methodology follows the style advocated by LCF-style theorem provers, i.e., it is based on inductive definitions and is computational in nature. The proof (i) uses simple computational means, only, (ii) basically is by construction, and (iii) reaches a constructively stronger conclusion than informal efforts. We believe the development is a first as far as formalized game theory goes.     

Elimination of fictitious penetrating rays from PO and hybridization with AFIM

Physical optics (PO) is an approximation method for high‐frequency scattering and diffraction problems. But PO fields are inaccurate in the shadow region where the source is screened by the scatter. Two key factors of the error for PO are (i) edge diffraction coefficients and (ii) existence of fictitious penetrating rays. The correction with respect to the former has been extensively investigated by many authors using various ray techniques such as GTD, UTD, and UAT. On the other hand, the latter was identified recently by the authors. This paper proposes novel PO‐based calculation procedures termed PO‐AF and PTD‐AF, where PO and Aperture Field Integration Method (AFIM) are merged with the help of special elementary diffraction coefficients. These can uniformly cover the whole angular region and only the error factor (ii) is removed in PO‐AF while both (i) and (ii) are removed in PTD‐AF. The theoretical backgrounds of PO currents are discussed in terms of field equivalence theorem and visualization of EM waves. Next, new methods are proposed and their validity is numerically demonstrated for 2D scattering problems of a strip, a corner reflector, and a cylinder of circular arc. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(2): 1–10, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20037     

可信性空间上基于复模糊变量的学习理论的关键定理

给出了可信性测度空间上复模糊变量定义及一些性质;给出了复模糊变量的经验风险泛函、期望风险泛函以及经验风险最小化原则严格一致收敛的定义。在此基础上给出并证明了基于复模糊变量的学习理论的关键定理,为系统建立可信性空间上的复统计学习理论奠定了理论基础。     

RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.     

函数S-粗集与规律F-隐藏

函数单向S-粗集(Function one direction singular rough sets)是用R-函数等价类定义的,函数是个规律;函数单向S-粗集具有规律特征、动态特征.利用函数单向S-粗集,给出规律F-隐藏概念,提出规律的F-隐藏定理,隐藏识别准则,给出规律的F-隐藏的应用.规律的F-隐藏是函数S-粗集中的一个新的应用研究方向,函数S-粗集是信息规律研究中的一个新理论与新工具.     

Efficient conditional probability theorem and importance sampling-based methods for global reliability sensitivity analysis

Global reliability sensitivity (GRS) analysis can measure the effect of random inputs on failure probability (FP). To efficiently solve GRS, two conditional probability theorem (CPT)-based methods are proposed by combining adaptive Kriging (AK) with importance sampling (IS) (CPT-AK-IS) and combining AK with Meta-IS (CPT-AK-Meta-IS) respectively. Firstly, differentiation approximation and CPT are used to convert the estimation of conditional probability density function (PDF), which is required by the existing Bayes theorem-based methods, into that of a series of probabilities. Secondly, GRS can be directly estimated by the failure samples of IS, while the existing Bayes theorem methods based on IS need to transform the failure samples of IS into those of original PDF. Both the first and second strategies can reduce the computational complexity of solving GRS. Thirdly, by selecting a suitable differentiation interval with a proposed adaptive strategy, the estimation of a series of probabilities can be accurately completed as a byproduct of one IS based simulation for solving FP without additional computational cost. Finally, by introducing AK into IS and Meta-IS, it can reduce the number of evaluating performance function and the size of candidate sample pool simultaneously. These novelties are sufficiently verified by the presented examples.     

Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-point boundary value problem

In this paper, we consider the following nonlinear fractional three-point boundary value problem