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An Automated Derivation of Łukasiewicz ' s CN from the Hilbert / Ackerman Grundzüge Sentential Calculus

Two logics are implicationally equivalent if the axioms and inference rules of each imply the axioms of the other. Characterizing the inferential equivalences of various formulations of the sentential calculi is thus foundational to the study of logic. Using an automated deduction system, I show that Łukasiewicz's CN can be derived from the sentential calculus, here called GTL, of Hilbert/Ackerman's Grundzüge der theoretischen Logik. Although each of these systems is known to imply the other, the proof presented here appears to be novel.