Sets of postulates for the logic of propositions
B. A. Bernstein · Transactions of the American Mathematical Society · 1926
Introduction.Boole | created the mathematical sciences now known as the logic of classes and the logic of propositions.! Peirce § and Schröder|| have perfected these sciences.The logic of classes now rests on rigorous, postulational foundations.Various sets of postulates, with consistency, independence, and sufficiency proved, have been worked out for that logic.% But no rigorous postulate sets exist for the logic of propositions.**The object of this paper is to supply such sets for this logic.My starting point is Schröder 's analysis of the logic, f f The propositional logic is the body of facts concerning the truth or falsity of propositions a, b, c, ■ • • and their combinations.Every proposition a is either true or else it is false.If true, we write a = 1 ; if false, we write a = 0. Every fact in this logic, symbolically expressed, is also a fact in the logic of classes consisting of the elements 0, 1 ; and conversely.With Schröder, therefore, I define the logic of propositions to be a two-element logic of classes.It is the algebra of truth-values 0, l.ft