The algebra of logic developed by Boole was not Boolean algebra. In this article we give a natural framework that allows one to easily reconstruct his algebra and see the difficulties it created for his successors. It is well known that modern Boolean algebra is connected with the work of George Boole [1815–1864], namely with his two books on a mathematical treatment of logic: • The Mathematica...

The aim of the study is to develop a numerical method for solution cubic nonlinear differential equations in which based on Boole polynomials. That form truncated series and gives approximate type. In this method, firstly, matrix serial set equation converted into system. By adding effect both conditions problem collocation points system equations, we obtain new equations. coefficients Boole-ba...

is a well-known formula from classical analysis giving a relation between the finite sum of values of a function f , whose first m derivatives are absolutely integrable on [a, n], and its integral, for a,m, n ∈ N, a < n. This elementary formula appears often in introductory texts [2, 17], usually in reference to a particular application—Stirling’s asymptotic formula. However, general approaches...

The collected works of English mathematics educator, Mary Boole, might be invaluable for education and curriculum research that attempts to understand the question: “what counts as knowing?” Even though it was written before 1916, Boole’s work allows curriculum researchers and teacher educators interested in the question to experience a significant shift in thinking. For example, in the followi...

For each word w in the Fibonacci lattices Fib(r) and Z (r) we partition the interval ^ 0; w] in Fib(r) into subposets called r-Boolean posets. In the case r = 1 those subposets are isomorphic to Boolean algebras. We also partition the interval ^ 0; w] in Z (r) into certain spanning trees of the r-Boolean posets. A bijection between those intervals is given in which each r-Boolean poset in Fib(r...

We address the basic meaning of apparent contradictions of quantum theory and probability frameworks as expressed by Bell’s inequalities. We show that these contradictions have their origin in the incomplete considerations of the premisses of the derivation of the inequalities. A careful consideration of past work, including that of Boole and Vorob’ev, has lead us to the formulation of extended...

This paper is more a series of notes than a scholarly treatise. It focuses on certain achieve‐ ments of Aristotle, Boole and Tarski. The notes presented here using concepts introduced or formalized by Tarski contribute toward two main goals: comparing Aristotle’s system with one Boole constructed intending to broaden and to justify Aristotle’s, and giving a modern perspective to both logics. ...

It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the model of Ivor Grattan-Guinness (1988 ), the tradition of the algebra of logic and the tradition of mathematical logic. They are represented by the developments going back to the British algebraist Georg...