On Foundations of the Three-Valued Logic

Abstract

At the root of two-valued logic we use there is the assumption, which is usually not formulated explicitly, but is a basic one, and which is called the principle of two-values. This principle in twovalued logic corresponds to the principle of contradiction and the principle of the excluded middle. However, the principle of the syllogism in the usual (conjunctively transitive) formulation, and the principle of contradiction, of the excluded middle are only "possible" in three-valued logic. From this, three-valued logic are connected with a modal functor such as 'M' to be called "possible" (möglich). Furthermore, some laws of two-valued logic are false in three-valued logic, among others the law (a=a') = 0. From this fact results the absence of antinomies in three-valued logic.Thus any of many-valued logic from three-valued to infinitely many-valued is a proper part or a proper sublogic of two-valued logic, and the latter is a superlogic of the former.