AbstractsPhilosophy & Theology

In this paper, we study the completeness property of some implication-negation fragments of propositional logics. By the phrase implication-negation fragment of a propositional logic, we understand the system consisting of all the theses which have implication and/or negation as their sole connectives in the said logic. This means, that we have to find a means to isolate, so to speak, all these theses and then axiomatize the resultant system. Our method of proof is by constructing a Gentzen type Sequenzen Kalkul which is strong enough to embrace all theses in the said logic. Since, Sequenzen Kalkul has a constructive character, every connective, once introduced, will remain in later sequents of the derivation.