Abstract

In some philosophical conceptions, statements are valued as true, false, senseless, or inconsistent. Falsehood logic FL4 makes it possible to operate correctly by such statements. Logic with falsehood operator FL4 is formulated. For FL4 metatheorems of consistency, deduction and completeness are fulfilled. Correlation between falsehood logic FL4 and four-valued Belnap’s logic and von Wright’s truth logic T"LM is considered. In FL4, the implication for Belnap’s logic is defined so that the truth-valued matrix of it is characterized for logic of tautological consequences Efde. Correlation between three-valued falsehood sublogic FL3N of FL4 and three-valued Kleene’s logic and Lukasiewicz’s logic is considered. Lukasiewicz’s three-valued logic is functionally equivalent to FL3N logic. Correlation between three-valued falsehood sublogic FL3B of FL4 and three-valued paraconsistent Priest’s logic is also considered.