Logics of Rejection: Two Systems of Natural Deduction

Logique Et Analyse 146:169-208 (1994)
This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two systems of natural deduction and prove them to be sound and complete. We conclude with a ‘Theorem of Inversion’.
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