This paper summarizes a mathematical model for characterizing hysteresis in ferroelectric materials. The model is based on the quanti cation of energy required to bend and translate domain walls and is developed in two steps. In the rst, the underlying anhysteretic polarization is quanti ed through constitutive equations derived using Boltzmann statistics. Three anhysteretic models are consider...

Quanti®ed statements are used in the resolution of a great variety of problems. Several methods have been proposed to evaluate statements of types I and II. The objective of this paper is to study these methods, by comparing and generalizing them. In order to do so, we propose a set of properties that must be ful®lled by any method of evaluation of quanti®ed statements, we discuss some existing...

In dynamic semantics three styles of quanti cation have been proposed that can be seen to involve two di erent ways of interpreting free and quanti ed variables: Variables as denoting single partial objects; Variables as ranging over a number of alternative total objects. I will show that the rst view leads to problems of underspeci cation and the second to problems of overspeci cation. I will ...

A combinatorial criterium is given when a monadic quantiier is expressible by means of universe-independent monadic quantiiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the HH artig quantiier is not deenable by monadic quantiiers. The techniques rely on Ramsey theory.

While numerous extensions of Cardelli and Wegner's calculus of polymorphism and subtyping, Kernel Fun, have been studied during the past decade, one quite simple one has received little attention: the addition of a minimal type Bot, dual to the familiar maximal type Top. We develop basic meta-theory for this extension. Although most of the usual properties of Kernel Fun (existence of meets and ...

With this notice, Frontiers states its awareness of concerns regarding a number of instances of failure to adequately cite or attribute credit appropriately within the above-referenced article. Prof. Theophile Godfraind and Prof. Olivier Feron, Chief Editors of the journal and specialty section respectively, will direct an investigation in full accordance with our procedures. The situation will...

In this paper, we de ne a rst-order logic CF 0 with strong negation and bounded classical quanti ers, which is a variant of Thomason's logic CF . For the logic CF 0, the usual Kripke formal semantics is dened based on situations, and a sound and complete axiomatic system is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof t...

The inexact information system is based on linguistic terms which have values lying in the interval [0; 1]. Imprecision has advantages, because fuzzy sets avoid the rigidity of conventional mathematical reasoning and computer programming. Fuzzy quanti ers are made explicit by means of fuzzy logic. Many systems, for example, complex biological processes, cannot be programmed in a precise way. Wi...