Deriving theory superposition calculi from convergent term rewriting systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1833, Issue , 2000, Pages 229-245

  Stuber, Jürgen ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMINERALIZATION; PATHOLOGY; THEOREM PROVING;

AUTOMATED THEOREM PROVER; AUTOMATED THEOREM PROVING; COMMUTATIVE RING; COMMUTATIVITY; DISTRIBUTIVITY; EQUATIONAL THEORY; ORDER RESTRICTION; TERM REWRITING SYSTEMS;

GROUP THEORY;

EID: 84937413155     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/10721975_16     Document Type: Conference Paper

References (34)

1. Baader, F. and Nipkow, T. (1998). Term rewriting and all that, Cambridge University Press, Cambridge, UK.
2. Bachmair, L. and Ganzinger, H. (1994a). Associative-commutative superposition. In N. Dershowitz and N. Lindenstrauss (eds), Proc. 4th Int. Workshop on Conditional and Typed Rewriting, LNCS 968, Springer, Jerusalem, pp. 1–14.
3. Bachmair, L. and Ganzinger, H. (1994b). Buchberger’s algorithm: A constraint-based completion procedure. Proc. 1st Int. Conf. on Constraints in Computational Logics, LNCS 845, Springer, Munich, Germany, pp. 285–301.
4. Bachmair, L. and Ganzinger, H. (1998). Equational reasoning in saturation-based theorem proving. Automated Deduction - A Basis for Applications. Volume 1, Kluwer, Dordrecht, The Netherlands, chapter 11, pp. 353–397.
5. Bachmair, L. and Tiwari, A. (1997). D-bases for polynomial ideals over commutative noetherian rings. In H. Comon (ed.), 8th Intl. Conf. on Rewriting Techniques and Applications, LNCS 1103, Springer, Sitges, Spain, pp. 113–127.
6. Bachmair, L., Ganzinger, H. and Stuber, J. (1995). Combining algebra and universal algebra in first-order theorem proving: The case of commutative rings. Proc. 10th Workshop on Specification of Abstract Data Types, LNCS 906, Springer, Santa Margherita, Italy, pp. 1–29.
7. Becker, T. and Weispfenning, V. (1993). Gröbner Bases: A Computational Approach to Commutative Algebra, Springer, Berlin.
8. Buchberger, B. and Loos, R. (1983). Algebraic simplification. Computer Algebra: Symbolic and Algebraic Computation, 2nd edn, Springer, pp. 11–43.
9. Buchberger, B. (1970). Ein algorithmisches Kriterium für die Lösbarkeit eines alge-braischen Gleichungssystems. Aequationes Mathematicae 4: 374–383.
10. Buchberger, B. (1987). History and basic features of the critical pair/completion procedure. Journal of Symbolic Computation 3: 3–38.
11. Bündgen, R. (1996). Buchberger’s algorithm: The term rewriter’s point of view. Theoretical Computer Science 159: 143–190.
12. Contejean, E. and Marché, C. (1996). CiME: Completion modulo E. Proc. 7th Int. Conf. on Rewriting Techniques and Applications, LNCS 1103, Springer, New Brunswick, NJ, USA, pp. 18–32.
13. Delor, C. and Puel, L. (1993). Extension of the associative path ordering to a chain of associative commutative symbols. Proc. 5th Int. Conf. on Rewriting Techniques and Applications, LNCS 690, Springer, pp. 389–404.
14. Dershowitz, N. and Jouannaud, J.-P. (1990). Rewrite systems. In J. van Leeuwen (ed.), Handbook of Theoretical Computer Science: Formal Models and Semantics, Vol. B, Elsevier/MIT Press, chapter 6, pp. 243–320.
15. Ganzinger, H. and Waldmann, U. (1996). Theorem proving in cancellative abelian monoids (extended abstract). 13th Int. Conf. on Automated Deduction, LNAI 1104, Springer, New Brunswick, NJ, USA, pp. 388–402.
16. Godoy, G. and Nieuwenhuis, R. (2000). Paramodulation with built-in abelian groups. To appear in LICS 2000.
17. Greendlinger, M. (1960). Dehn’s algorithm for the word problem. Communications on Pure and Applied Mathematics 13: 67–83.
18. Jouannaud, J.-P. and Kirchner, H. (1986). Completion of a set of rules modulo a set of equations. SIAM Journal on Computing 15(4): 1155–1194.
19. Kandri-Rody, A. and Kapur, D. (1988). Computing a Gr¨obner basis of a polynomial ideal over a Euclidean domain. Journal of Symbolic Computation 6: 19–36.
20. Le Chenadec, P. (1986). Canonical Forms in Finitely Presented Algebras, Pitman, London.
21. Marché, C. (1996). Normalised rewriting: an alternative to rewriting modulo a set of equations. Journal of Symbolic Computation 21: 253–288.
22. Nieuwenhuis, R. and Rubio, A. (1997). Paramodulation with built-in AC-theories and symbolic constraints. Journal of Symbolic Computation 23: 1–21.
23. Peterson, G. E. and Stickel, M. E. (1981). Complete sets of reductions for some equational theories. Journal of the ACM 28(2): 233–264.
24. Stuber, J. (1996). Superposition theorem proving for abelian groups represented as integer modules. In H. Ganzinger (ed.), Proc. 7th Int. Conf. on Rewriting Techniques and Applications, LNCS 1103, Springer, New Brunswick, NJ, USA, pp. 33–47.
25. Stuber, J. (1997). Strong symmetrization, semi-compatibility of normalized rewriting and first-order theorem proving. In M. P. Bonacina and U. Furbach (eds), Proc. Int. Workshop on First-Order Theorem Proving. RISC-Linz Report 97-50, Research Institute for Symbolic Computation, Linz, Austria, pp. 125–129.
26. Stuber, J. (1998a). Superposition theorem proving for abelian groups represented as integer modules. Theoretical Computer Science 208(1–2): 149–177.
27. Stuber, J. (1998b). Superposition theorem proving for commutative rings. In W. Bibel and P. H. Schmitt (eds), Automated Deduction - A Basis for Applications. Volume 3. Applications, Kluwer, Dordrecht, The Netherlands, chapter 2, pp. 31–55.
28. Stuber, J. (1999a). Superposition Theorem Proving for Commutative Algebraic Theories, Dissertation, Technische Fakultät, Universit¨at des Saarlandes, Saarbru¨cken. Submitted.
29. Stuber, J. (1999b). Theory path orderings. Proc. 10th Int. Conf. on Rewriting Techniques and Applications (RTA-99), LNCS 1631, Springer, Trento, Italy, pp. 148–162.
30. Vigneron, L. (1994). Associative-commutative deduction with constraints. Proc. 12th Int. Conf. on Automated Deduction, LNCS 814, Springer, Nancy, France, pp. 530–544.
31. Waldmann, U. (1997). Cancellative Abelian Monoids in Refutational Theorem Proving, Dissertation, Universität des Saarlandes, Saarbru¨cken.
32. Waldmann, U. (1998). Superposition for divisible torsion-free abelian groups. Proc. 15th Int. Conf. on Automated Deduction (CADE-15), LNAI 1421, Springer, Townsville, Australia, pp. 144–159.
33. Wertz, U. (1992). First-order theorem proving modulo equations. Technical Report MPI-I-92-216, Max-Planck-Institut für Informatik, Saarbrücken.
34. Zhang, H. (1993). A case study of completion modulo distributivity and abelian groups. Proc. 5th Int. Conf. on Rewriting Techniques and Applications, LNCS 690, Springer, Montreal, pp. 32–46.