Solution of the Robbins Problem
- William Mccune
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
In this article we show that the three equations known as commutativity,associativity, and the Robbins equation are a basis for the variety ofBoolean algebras. The problem was posed by Herbert Robbins in the 1930s. Theproof was found automatically by EQP, a theorem-proving program forequational logic. We present the proof and the search strategies thatenabled the program to find the proof.
- Bachmair, L., Ganzinger, H., Lynch, C. and Snyder, W.: Basic paramodulation and superposition, in D. Kapur (ed.), Proc. 11th Int. Conf. on Automated Deduction, Lecture Notes in Artificial Intelligence, Vol. 607, Springer-Verlag, 1992, pp. 462–476.
- Burris, S.: Correspondence, November 1996.
- Henkin, L., Monk, J. D. and Tarski, A.: Cylindric Algebras, Part I, North-Holland, 1971.
- Hullot, J.-M.: Canonical forms and unification, in R. Kowalski and W. Bibel (eds), Proc. CADE-5, LNCSVol. 87, Springer-Verlag, Berlin, 1980, pp. 318–334.
- Huntington, E. V.: Boolean algebra. A correction, Trans. AMS 35(1933), 557–558.
- Huntington, E. V.: New sets of independent postulates for the algebra of logic, with special reference to Whitehead and Russell’s Principia Mathematica, Trans. AMS 35(1933), 274–304.
- Kapur, D., Musser, D. and Narendran, P.: Only prime superpositions need be considered in the Knuth–Bendix completion procedure, J. Symbolic Computation 6(1988), 19–36.
- Kapur, D. and Zhang, H.: RRL: Rewrite Rule Laboratory user’s manual, Technical Report 89-03, Department of Computer Science, University of Iowa, 1989.
- Knuth, D. and Bendix, P.: Simple word problems in universal algebras, in J. Leech (ed.), Computational Problems in Abstract Algebras, Pergamon Press, Oxford, 1970, 263–297.
- McCune, W.: OTTER 3.0 Reference Manual and Guide, Technical Report ANL-94/6, Argonne National Laboratory, Argonne, Ill., 1994.
- McCune, W.: 33 basic test problems: A practical evaluation of some paramodulation strategies, in Robert Veroff (ed.), Automated Reasoning: Essays in Honor of Larry Wos, Chapter 5. MIT Press, 1997. To appear.
- McNulty, G. F.: Undecidable properties of finite sets of equations, J. Symbolic Logic 41(1976), 589–604.
- Niewenhuis, R. and Rubio, A.: Theorem proving with ordering and equality constrained clauses, J. Symbolic Computation 19(4) (1995), 321–351.
- Robbins, H.: Phone conversation, October 1996.
- Stickel, M.: A unification algorithm for associative-commutative functions, J. ACM 28(3) (1981), 423–434.
- Winker, S.: Robbins algebra: Conditions that make a near-Boolean algebra Boolean, J. Automated Reasoning 6(4) (1990), 465–489.
- Winker, S.: Absorption and idempotency criteria for a problem in near-Boolean algebras, J. Algebra 153(2) (1992), 414–423.
- Wos, L., Overbeek, R., Lusk, E. and Boyle, J.: Automated Reasoning: Introduction and Applications, 2nd edition, McGraw-Hill, New York, 1992.
- Solution of the Robbins Problem
Journal of Automated Reasoning
Volume 19, Issue 3 , pp 263-276
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- associative-commutative unification
- Boolean algebra
- equational logic
- Robbins algebra
- Robbins problem
- Industry Sectors
- William Mccune (1)
- Author Affiliations
- 1. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Il, 60439