Logics of rejection: Two systems of natural deduction

Allard M Tamminga

Abstract


This paper contains two systems of natural deduction for the rejection of non-tautologies of Classical Propositional Logic. The first system is correct and complete with respect to the body of all non-tautologies, the second system is correct and complete with respect to the body of all contradictions. The second system is a subsystem of the first. We begin with an historical synopsis of the development of the theories of rejection for the classical logic of propositions, taking our starting-point from the theories of their 'founding father', Jan Lukasiewicz. Subsequently, the systems of natural deduction are set forth and their correctness and completeness is showed. We shall conclude with an interesting 'Theorem of Inversion'.

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