New uses of linear arithmetic in automated theorem proving by induction

Journal of Automated Reasoning

Volumn 16, Issue 1-2, 1996, Pages 39-78

  Kapur, Deepak ^a   Subramaniam, M ^a  

^a State University of New York   (United States)

Author keywords

Automated theorem proving; Generalization; Heuristics; Induction; Linear arithmetic; Presburger arithmetic; Semantic unification

Indexed keywords

AUTOMATION; COMPUTATIONAL LINGUISTICS; DECISION THEORY; DIGITAL ARITHMETIC; HEURISTIC METHODS; LOGIC PROGRAMMING; NUMBER THEORY; NUMERICAL METHODS;

FACTORIZATION THEOREM; GENERALIZATION; INDUCTION; PRESBURGER ARITHMETIC; PROOF MANAGEMENT SYSTEM; REWRITE RULE LABORATORY; SEMANTIC UNIFICATION;

THEOREM PROVING;

EID: 0030101018     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00244459     Document Type: Article

References (13)

1. Boyer, R. S. and Moore, J S.: A Computational Logic, ACM Monographs in Computer Science, 1979.
2. Boyer, R. S. and Moore, J S.: A Computational Logic Handbook, Academic Press, New York, 1988.
3. Boyer, R. S. and Moore, J S.: Integrating decision procedures into heuristic theorem provers: A case study of linear arithmetic, Machine Intelligence 11 (1988), 83-157.
4. Dershowitz, N.: Termination of rewriting, J. Symbolic Computation 3 (1987), 69-116.
5. Jouannaud, J.-P. and Kounalis, E.: Automatic proofs by induction in theories without constructors, Information and Computation 82 (1989), 1-33.
6. Kapur, D.: An automated tool for analyzing completeness of equational specifications, in Proc. Int. Symp. Software Testing and Analysis (ISSTA), Seattle, August 1994, pp. 28-43.
7. Kapur, D., Musser, D. R., and Nie, X.: An overview of the Tecton proof system, in Theoret. Computer Science Journal, special issue on Formal Methods in Databases and Software Engineering (ed. V. Alagar), Vol. 133, October 1994, pp. 307-339.
8. Kapur, D., Narendran, P., Rosenkrantz, D., and Zhang, H.: Sufficient-completeness, quasi-reducibility and their complexity, Acta Informatica 28 (1991), 311-350.
9. Kapur, D. and Nie, X.: Reasoning about numbers in Tecton, in Proc. 8th Int. Symp. Methodologies for Intelligent Systems (ISMIS'94), Charlotte, NC, October 1994, pp. 57-70.
10. Kapur, D. and Zhang, H.: An overview of Rewrite Rule Laboratory (RRL), J. Computer Math. Appl. 29(2) (1995), 91-114.
11. Walther, C.: Combining induction axioms by machine, Proc. 12th Int. Joint Conf. Artificial Intelligence, Chambery, France, 1993.
12. Zhang, H.: Reduction, superposition and induction: Automated reasoning in an equational logic, Ph.D. Thesis, Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, 1988.
13. Zhang, H., Kapur, D., and Krishnamoorthy, M. S.: A mechanizable induction principle for equational specifications, in Proc. 9th Int. Conf. Automated Deduction (CADE-9), Argonne, IL, LNCS 310, Springer-Verlag, 1988, pp. 250-265.