On an implication function in many-valued systems of logic

Abstract

In a paper J. Łukasiewicz and A. Tarski study the systems arising out of the implication function C (x, y) = min(1, 1 – x + y) and the negation function Nx = 1 – x, where x, y are real numbers between 0 and 1 inclusive. Let us then write Сxy = min(1, 1 – x + y) and Nx = 1 – x. (1)In this note we shall consider another implication function, namely С′xy = ССNxyy, (2)