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.     

Accurate higher-order analytical approximate solutions to nonconservative nonlinear oscillators and application to van der Pol damped oscillators

In general, this paper deals with general nonlinear oscillations of a nonconservative and single degree-of-freedom system with odd nonlinearity and, in particular, it presents accurate higher-order analytical approximate solutions to van der Pol damped nonlinear oscillators having odd nonlinearity and the Rayleigh equation. By combining the linearization of the governing equation with harmonic balancing and the method of averaging, we establish accurate analytical approximate solutions for the general weakly damped nonlinear systems. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. The combination of these two methods results in very accurate transient response of the periodic solution. In addition and for the first time, this paper also presents a method for deducing fourth-, fifth- and higher-order linearized governing equations from the lower-order equations without the requirement of formulating the problem from the first principle. Three examples including the van der Pol damped nonlinear oscillator are presented to illustrate the excellent agreement with approximate solution using the exact frequency.     

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.     

Evaluation codes at singular points of algebraic differential equations

We use the special geometry of singular points of algebraic differential equations on the affine plane over finite fields to study the main features and parameters of error correcting codes giving by evaluating functions at sets of singular points. In particular, one gets new methods to construct codes with designed minimum distance. This work was partially supported by MCyT BFM2001-2251.     

Dynamic averaging and foraging decisions in horses (Equus callabus).

The variability of most environments taxes foraging decisions by increasing the uncertainty of the information available. One solution to the problem is to use dynamic averaging, as do some granivores and carnivores. Arguably, the same strategy could be useful for grazing herbivores, even though their food renews and is more homogeneously distributed. Horses (Equus callabus) were given choices between variable patches after short or long delays. When patch information was current, horses returned to the patch that was recently best, whereas those without current information matched choices to the long-term average values of the patches. These results demonstrate that a grazing species uses dynamic averaging and indicate that, like granivores and carnivores, they can use temporal weighting to optimize foraging decisions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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     

Choosing OWA operator weights in the field of Social Choice

One of the most important issues in the theory of OWA operators is the determination of associated weights. This matter is essential in order to use the best-suited OWA operator in each aggregation process. Given that some aggregation processes can be seen as extensions of majority rules to the field of gradual preferences, it is possible to determine the OWA operator weights by taking into account the class of majority rule that we want to obtain when individuals do not grade their pairwise preferences. However, a difficulty with this approach is that the same majority rule can be obtained through a wide variety of OWA operators. For this reason, a model for selecting the best-suited OWA operators is proposed in this paper.     

Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation

Abstract. Large sample properties of the least‐squares and weighted least‐squares estimates of the autoregressive parameter of the explosive random‐coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least‐squares estimator is inconsistent whereas the weighted least‐squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian. Conditional asymptotics on the event that a certain limiting random variable is non‐zero is also discussed.     

Stratified institutions and elementary homomorphisms

For conventional logic institutions, when one extends the sentences to contain open sentences, their satisfaction is then parameterized. For instance, in the first-order logic, the satisfaction is parameterized by the valuation of unbound variables, while in modal logics it is further by possible worlds. This paper proposes a uniform treatment of such parameterization of the satisfaction relation within the abstract setting of logics as institutions, by defining the new notion of stratified institutions. In this new framework, the notion of elementary model homomorphisms is defined independently of an internal stratification or elementary diagrams. At this level of abstraction, a general Tarski style study of connectives is developed. This is an abstract unified approach to the usual Boolean connectives, to quantifiers, and to modal connectives. A general theorem subsuming Tarski's elementary chain theorem is then proved for stratified institutions with this new notion of connectives.