For over a century, the study of logic has focused on the algebra of logical statements. This work, first performed by George Boole, has led to the development of modern computers, and was shown by Richard T. Cox to be the foundation of Bayesian inference. Meanwhile the logic of questions has been much neglected. For our computing machines to be truly intelligent, they need to be able to ask re...

It has been proposed that all M -channel paraunitary (PU) multirate filter banks over GF(2) can be described using the product of basic lattice blocks. In this paper this conjecture is proven by considering a redefinition of degree-0 lattice blocks. A factorisation algorithm that factors all degree-J PU filter banks over GF(2) is presented. In the course of this work M -channel type-I matrices ...

There was a time when Logic was the dominant paradigm for human reasoning. As George Boole put it around one hundred and fifty years ago, Logic was synonymous with the “Laws of Thought”. Later, for most of the latter half of the twentieth century, it was the mainstream of Artificial Intelligence. But then it all went wrong. Artificial Intelligence researchers, frustrated by the lack of progress...

We solve two fundamental problems of probabilistic reasoning: given a finite set of conditional probability assessments, how to determine whether the assessments are mutually consistent, and how to determine what they imply about the conditional probabilities of new events? These problems were posed in 1854 by George Boole, who gave a partial solution using algebraic methods. The two problems a...

George Boole (1815–1864) is rightly known as a logician, the author of an algebra logic, even if he did not conceive it quite in same way we know it. The calculus on classes and propositions, that set out to be equivalent, were at core his logic. After more than twenty centuries where logic was associated analysis language, handled for first time with mathematical symbols. However, Boole’s one ...

The apparition of Fuzzy Logic [10] has had a double repercussion on scientific research, and has provoked two types of reactions. From a theoretical point of view, it is indeed a very useful generalization of the classical Set Theory proposed by Boole and Cantor, in this way making possible our analysis of uncertainty. But unfortunately, in his first steps it had to avoid the assaults of routin...

The word, Boolean, was derived from the name of a British mathematician, George Boole, as a result of his classical work on logic. Boolean algebra can be defined as a set, whose members have two possible values, with two binary operators and one unary operator, satisfying the properties of commutativity, associativity, distributivity, existence of identity and complement. Boolean algebra has im...

Classical logic is the study of " safe " formal reasoning. Western Philosophers developed classical logic over a period of thirty-three centuries after its introduction in the form of syllogistic by Aristotle [1] in the third century B. C. Beginning in the nineteenth century with De Morgan [2] and Boole [3], responsibility for the development of classical logic moved from the philosophical to t...

Polynomizing is a term that intends to describe the uses of polynomiallike representations as a reasoning strategy and as a tool for scientific heuristics. I show how proof-theory and semantics for classical and several non-classical logics can be approached from this perspective, and discuss the assessment of this prospect, in particular to recover certain ideas of George Boole in unifying log...