Трехзначные изоморфы классической логики.

Abstract

Three-valued isomorph of the classic propositional logic $C_2$ is a set of three-valued connectives that verifies all classic axioms based on corresponding binary connectives and modus ponens. This paper deals with the implicative-negative case of such sets. An essential theorem concerning properties of three-valued isomorphs of $C_2$ is proven. In every isomorph, implication is only false (i.e. takes a non-designated value) iff an antecedent is true (i.e. takes a designated value) and a consequent is false. And the negation is only false iff a corresponding propositional variable takes a designated value. Once we have proved such a theorem we are able to show that every threevalued $C_2$ isomorph is consistent, count the total amount of three-valued $C_2$ isomorphs and devise a minimal condition for a three-valued logic to contain an isomorph of $C_2$.