Abstract
This paper shows how the automated theorem-proving program OTTER was used to discover new axiomatizations, including single axioms, for the left group and righ group calculi. J. A. Kalman's original axiomatizations of the two calculi each contain five axioms. Three of Kalman's axioms (L1, L4, and L5) for the left group calculus were shown to be dependent on the remaining two axioms. Four of Kalman's axioms (R1, R3, R4, and R5) for the right group calculus were shown to be dependent on the remaining axiom. Alternative simpler axiomatizations were discovered for both calculi, including a single axiom for the left group calculus and five additional single axioms for the right group calculus. The program OTTER was vital in discovering candidate axiomatizations as well as in finding proofs of new axiomatizations. All of the relevant OTTER proofs are included.
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This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.
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Mccune, W.W. Automated discovery of new axiomatizations of the left group and right group calculi. J Autom Reasoning 9, 1–24 (1992). https://doi.org/10.1007/BF00247824
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DOI: https://doi.org/10.1007/BF00247824