CHAPTER 3 - MATRIX FORMULATION OF LOGIC

Abstract

This chapter discusses the computational capabilities of logic by interpreting logic connectives as matrix operators acting in two adjoining spaces of logic vectors. In first step toward matrix formulation of logic, the truth-tables of the binary Boolean functions are regrouped and presented in the form of square tables. Each table in the square representations of the Boolean functions has its own reference variables: x is indicated in the leftmost column, and y in the topmost row. The four different values inside the tables are the values that are yielded by the corresponding Boolean function. Matrix logic is founded on the basis operator postulate that instead of viewing the given truth-tables as a convenient illustration, interprets the tables as mathematical objects. The vector space formalism offers a concise, consistent notation that ideally suits to the needs of matrix logic.