Short single axioms for Boolean algebra

Journal of Automated Reasoning

Volumn 29, Issue 1, 2002, Pages 1-16

  McCune, William ^a   Veroff, Robert ^b   Fitelson, Branden ^c   Harris, Kenneth ^a   Feist, Andrew ^d   Wos, Larry ^a  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b MSC01 1070   (United States)

^c STANFORD UNIVERSITY   (United States)

^d DUKE UNIVERSITY   (United States)

Author keywords

Boolean algebra; Sheffer stroke; Single axiom

Indexed keywords

AUTOMATA THEORY; COMPUTER SIMULATION; CONFORMAL MAPPING; MATHEMATICAL MODELS; SEMANTICS; THEOREM PROVING;

AUTOMATED DEDUCTION TECHNIQUES; AXIOMIZATION; SHEFFER STROKE; SINGLE AXIOMS;

BOOLEAN ALGEBRA;

EID: 0036624926     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020542009983     Document Type: Article

References (20)

1. Avenhaus, J.: Correspondence by electronic mail, 2000.
2. Hillenbrand, T., Buch, A., Vogt, R. and Löchner, B.: Waldmeister, J. Automated Reasoning 18(2) (1997), 265-270.
3. Kunen, K.: Single axioms for groups, J. Automated Reasoning 9(3) (1992), 291-308.
4. McCune, W.: Otter, http://www.mcs.anl.gov./AR/otter/, 1994.
5. McCune, W.: Otter 3.0 reference manual and guide, Technical Report ANL-94/6, Argonne National Laboratory, Argonne, IL, 1994.
6. McCune, W.: Solution of the Robbins problem, J. Automated Reasoning 19(3) (1997), 263-276.
7. McCune, W.: Single axioms for Boolean algebra, Tech. Memo ANL/MCS-TM-243, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 2000.
8. McCune, W.: MACE 2.0 reference manual and guide, Tech. Memo ANL/MCS-TM-249, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 2001.
9. McCune, W. and Shumsky, O.: IVY: A preprocessor and proof checker for first-order logic, in M. Kaufmann, P. Manolios and J. Moore (eds), Computer-Aided Reasoning: ACL2 Case Studies, Kluwer Academic Publishers, 2000, Chapt. 16.
10. Meredith, C. A.: Equational postulates for the Sheffer stroke, Notre Dame J. Formal Logic 10(3) (1969), 266-270.
11. Meredith, C. A. and Prior, A. N.: Equational logic, Notre Dame J. Formal Logic 9 (1968), 212-226.
12. Padmanabhan, R. and McCune, W.: Single identities for ternary Boolean algebras, Comput. Math. Appl. 29(2) (1995), 13-16.
13. Padmanabhan, R. and Quackenbush, R. W.: Equational theories of algebras with distributive congruences, Proc. Amer. Math. Soc. 41(2) (1973), 373-377.
14. Sheffer, H.: A set of five independent postulates for Boolean algebras, with application to logical constants, Trans. Amer. Math. Soc. 14(4) (1913), 481-488.
15. Veroff, R.: Using hints to increase the effectiveness of an automated reasoning program: Case studies, J. Automated Reasoning 16(3) (1996), 223-239.
16. Veroff, R.: Short 2-bases for Boolean algebra in terms of the Sheffer stroke, Technical Report TR-CS-2000-25, Computer Science Department, University of New Mexico, Albuquerque, NM, 2000.
17. Wolfram, S.: Correspondence by electronic mail, 2000.
18. Wos, L.: Searching for circles of pure proofs, J. Automated Reasoning 15(3) (1995), 279-315.
19. Wos, L. and Pieper, G.: A Fascinating Country in the World of Computing: Your Guide to Automated Reasoning, World Scientific, Singapore, 1999.
20. Zhang, J. and Zhang, H.: SEM: A system for enumerating models, in Proc. IJCAI-95, Vol. 1, 1995, pp. 298-303.