AN ALGEBRAIC APPROACH TO LOGICS IN RESEARCH

1. A motivation for algebraic approaches to logics To realize the importance of the research work of Helena Rasiowa and Cecylia Rauszer in the area of algebraic methods in logics let us recall Got-tfried Wilhelm Leibniz. In [3] he wrote “Things are like numbers”. By this he meant that statements about complex things can be derived from statements about their simpler constituents by a process of combination analogous to arithmetic calculation on numbers. An algebraic calculation itself should be done by a machine. Thus he proposed: “It is unworthy of excellent [persons] to lose hours like slaves in the labor of calculation which could be safely relegated to anyone else if machines were used ” [7]. Having this in mind, he invented a device known as the Leibniz wheel for automatic addition, subtraction, multiplication, and division. Leibniz attached great significance to his vision of reducing human reasoning to algebraic calcu-lation, saying: “Nobody else, I believe, noticed this, otherwise... he would drop everything to focus on this subject, because a man cannot achieve any-thing greater ” [5]. It turned out that applications of algebraic calculus and machines to problem solving is very difficult. Current approaches are based on applications of Boolean algebra (or their modifications). The strong in-fluence of the Polish School of Logic is worth mentioning here, especiall