The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, since they are not dual. This paper offers them attention, comming to the following conclusions: some kind of hardly describable ”local preduality” still makes pos...

Authors: David Gravette, Pharm.D. Candidate, Harrison School of Pharmacy, Auburn University; Morgan Luger, Pharm.D. Candidate, Harrison School of Pharmacy, Auburn University; Jay Moulton, Pharm.D. Candidate, Harrison School of Pharmacy, Auburn University; Wesley T. Lindsey, Pharm.D., Associate Clinical Professor of Pharmacy Practice, Drug Information and Learning Resource Center, Harrison Schoo...

The importance of organizational-stakeholder relationships has and continues to be of interest in the organizational studies literature. The relevance of this topic is even greater given the recent governance failures involving Enron, Tyco, and WorldCom. Indeed, an excessive emphasis on stockholders is blamed for the neglect of other legitimate stakeholder groups. We should acknowledge that the...

Abstract. A new form of α-compactness is introduced in L-topological spaces by α-open L-sets and their inequality where L is a complete de Morgan algebra. It doesn’t rely on the structure of the basis lattice L. It can also be characterized by means of α-closed L-sets and their inequality. When L is a completely distributive de Morgan algebra, its many characterizations are presented and the re...

1. Set Theory and Basic Probability Properties Set Theory and Events The union of sets A and B: x ∈ A ∪B if and only if x ∈ A or x ∈ B The intersection of sets A and B: x ∈ A ∩B if and only if x ∈ A and x ∈ B The complement of a set A: x ∈ A if and only if x / ∈ A The difference between sets A and B: x ∈ A−B if and only if x ∈ A and x / ∈ B A collection of sets A1, ..., AN is mutually exclusive...

Multi-valued model-checking is an extension of classical model-checking to reasoning about systems with uncertain information, which are common during early design stages. The additional values of the logic are used to capture the degree of uncertainty. In this paper, we show that the multi-valued -calculus model-checking problem is reducible to several classical model-checking problems. The re...

We give a new and improved proof that the shrinkage exponent of De Morgan formulae is 2. Namely, we show that for any Boolean function f : {−1, 1} → {−1, 1}, setting each variable out of x1, . . . , xn with probability 1 − p to a randomly chosen constant, reduces the expected formula size of the function by a factor of O(p). This result is tight and improves the work of H̊astad [H̊as98] by removi...

In my paper [3], recently published in this Journal, I study several aspects of the relations between Belnap's logic B and the class DM of De Morgan lattices. Some of these relations concern a Gentzen system for Belnap's logic, denoted by G B , which was introduced in 1988 by my colleague Ventura Verdú and me (see [5] and [6]); indeed, the study of this Gentzen system within the theory of full ...

Description of the pairs 〈low approximation, upper approximation〉 of rough sets is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed. Then some general algebras can be selected to describe the pairs of rough sets. The most famous rough algebras are Rough Double Stone Algebra...

Marcos Curty, Marc Jofre, Valerio Pruneri, and Morgan W. Mitchell 1 Escuela de Ingenieŕıa de Telecomunicación, Department of Signal Theory and Communications, University of Vigo, Campus Universitario, 36310 Vigo, Pontevedra, Spain 2 ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain 3 ICREA-Institució Catalana de Recerca i Estudis Avançats...