Abstract
We present new results in axiomatic group theory obtained by using automated deduction programs. The results include single axioms, some with the identity and others without, for groups of exponents 3, 4, 5, and 7, and a general form for single axioms for groups of odd exponent. The results were obtained by using the programs in three separate ways: as a symbolic calculator, to search for proofs, and to search for counterexamples. We also touch on relations between logic programming and automated reasoning.
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
W. McCune. Otter 2.0 Users Guide. Tech. Report ANL-90/9, Argonne National Laboratory, Argonne, IL, March 1990.
W. McCune. Automated discovery of new axiomatizations of the left group and right group calculi. Preprint MCS-P220-0391, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1991. To appear in J. Automated Reasoning.
W. McCune. Single axioms for groups and Abelian groups with various operations. Preprint MCS-P270-1091, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1991.
W. McCune. What's New in Otter 2.2. Tech. Memo ANL/MCS-TM-153, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, July 1991.
W. McCune and L. Wos. Experiments in automated deduction with condensed detachment. Preprint MCS-P237-0491, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1991. To appear in proc. CADE-11, Springer-Verlag LNAI.
B. H. Neumann. Another single law for groups. Bull. Australian Math. Soc., 23:81–102, 1981.
J. Slaney. Finder, finite domain enumerator: Version 1.0 notes and guide. Tech. Report TR-ARP-10/91, Automated Reasoning Project, Australian National University, Canberra, Australia, 1991.
L. Wos and W. McCune. Automated theorem proving and logic programming: A natural symbiosis. Journal of Logic Programming, 11(1):1–53, July 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McCune, W., Wos, L. (1992). Application of automated deduction to the search for single axioms for exponent groups. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013055
Download citation
DOI: https://doi.org/10.1007/BFb0013055
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55727-2
Online ISBN: 978-3-540-47279-7
eBook Packages: Springer Book Archive