We propose an approach for decomposing Boolean satisfiability problems while extending recent results of [12] on solving Boolean systems of equations. Developments in [12] were aimed at the expansion of functions f in orthonormal (ON) sets of base functions as a generalization of the Boole-Shannon expansion and the derivation of the consistency condition for the equation f = 0 in terms of the e...

This article explores the ideas that went into George Boole’s development of an algebra for logic in his book The Laws of Thought. The many theories that have been proposed to explain the origins of his algebra have ignored his wife Mary Boole’s claim that he was deeply influenced by Indian logic. This paper investigates this claim and argues that Boole’s focus was more than a framework for pro...

Prior Analytics by the Greek philosopher Aristotle (384– 322 BCE) and Laws of Thought by the English mathematicianGeorge Boole (1815 – 1864) are the twomost important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and ...

We give examples of piecewise linear random interval maps satisfying arcsine and Darling–Kac laws, which are analogous to Thaler’s Aaronson’s laws for the Boole transformation. They constructed by switch two with attracting or repelling fixed points, behave as if they were indifferent points a deterministic map.

In this note, we outline a definition of propositional manifold and logical cohomology. An application is also considered for mathematics, two Boole algebras of mathematical propositions are non equivalent if their two cohomologies are not isomorphic.

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Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier inequalities presented by Boole and the findings of Vorob’ev as related to these inequalities. These findings together with a space-time generalization of Boole’s e...

We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases in a general approach to approximation that also encompasses Taylor sums. Here we give additional details of the construction.