This article is placed in the general frame of philosophy of information and it attempts to present a rarely mentioned application of Boolean system to the reduction of logic to mathematics in opposition to the widely known initiative of reduction of mathematics to logic (Frege, Russell, Wittgenstein, Godel). It concerns the transformation of categorical propositions to equivalent algebraic equations aiming at the extraction of some types of valid logical structures, including inversion formulae and syllogism schemata, through elimination and reduction techniques, presented in ‘Laws of Thought’ of George Boole.