Complementary logics for classical propositional languages
| Abstract | In an earlier paper I introduced a complete axiomatization of classical non-tautologies based essentially on Lukasiewicz’s rejection method. The present paper provides a new, Hilbert-type axiomatization (along with related systems to axiomatize classical contradictions, non-contradictions, contingencies and non-contingencies respectively). This new system is mathematically less elegant, but the format of the inferential rules and the structure of the completeness proof possess some intrinsic interest and suggests instructive comparisons with the logic of tautologies. | |||||||||
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