Sentential Falsehood Logic FL4 :: Philosophy Philosophical Logical Papers

Sentential refutation Logic FL4ABSTRACT In rough philosophical conceptions, statements are valued as sure, false, senseless (neither true nor false), or inconsistent. Falsehood system of 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. correlational statistics mingled with falsehood logic FL4 and four-valued Belnaps logic and von Wrights integrity logic TLM is rolled. In FL4, the implication for Belnaps 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 Kleenes logic and Lukasiewiczs logic is considered. Lukasiewiczs three-valued logic is functionally equivalent to FL3N logic. Correlation between three-valued falsehood sublogic FL3B of FL4 and three-valued paraconsistent Priests logic is also considered. The construction of falsehood logic FL4 (1) and its analysis dissolvent the question about the use of truth and falsehood notions. In some philosophical conceptions statements are valued as true, false, senseless (neither true nor false), inconsistent. Falsehood logic FL4 makes it possible to operate correctly by such statements.The primary(prenominal) principles of falsehood logic FL4 are as follows 1. The notion of falsehood bequeath be considered as applied only to strong beliefs of the following form strong belief S is false (in symbols (- S) ). The proposition (- S) is a proposition about falsehood of the sentence S and it is a proposition in a metalanguage related to the language in which a sentence S is formulated.The set of propositions of language, metalanguage, metametalanguage and so on is considered as a whole. And one can operate with these propositions (viz. S, (- S), (- S(- S)), ...) simultaneously in the language of FL4.2. We shall consider t he notion of falsehood as a primitive one which leave alone be used as a logical operator in this formal system.3. The sentence (- S) is always either true or false, trance the sentence S may have other truth-values than true or false. In other words, the laws of classical logic are valid for sentence (- S), but need not to be valid for sentence S. 4. Sentences with the implication depart be evaluated in standard way. Let (S1 S2) stands for S1 implies S2.(S1 S2) is true iff S1 is false or S2 is true.(S1 S2) is false iff S1 is true and S2 is false.