The Algebra of Boole

Abstract:

George Boole introduced Boolean algebra in 1847 and since then it has played a central role in various areas such as logic circuit design, complexity theory and propositional logic. The conventional Boolean Algebra has three basic operations with them being, conjunction, disjunction and negation. In this talk, we will explore a different framework, which we call the Algebra of Boole that utilises only two operations, the antivalence and the conjunction operation over the Boolean ring. We will see that the Algebra of Boole leads to a simpler framework to represent Boolean functions. Furthermore, we will also see that there is a connection between the Mobius function from the theory of posets with the Algebra of Boole.