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Equality Reasoning with Equality-paths

  • Conference paper
GWAI-85

Part of the book series: Informatik-Fachberichte ((2252,volume 118))

Abstract

The theoretical and practical problems of equality reasoning in Automated Deduction are notorious. A new method is presented to cope with the huge search space usually involved with equality. Starting from an empty graph a production system constructs graphs (equality-paths) which represent solutions for simpler problems defined by abstraction. These graphs contain global information and are plans for guiding the search for a proof of the original problem, represented in the final graph. The construction of equality-paths is based on the idea to search for the differences between two terms by seperating toplevel symbol and subterms of a functional term. For a further reduction of the search space some technical improvements are implemented including demodulation and a matching of termpairs using theory-matching algorithms for the cases of commutativity, associativity and a combination of both.

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References

  1. R. Anderson: Completeness results for E-resolution. Proc. Spring Joint Conf., 1970, 653–656

    Google Scholar 

  2. K.H. Blasius: Equality-Reasoning in clause graphs. Proc. IJCAI, 1963, 936–939

    Google Scholar 

  3. K.H. Blasius: Correctness and Completeness of the equality-path construction method, (forthcoming)

    Google Scholar 

  4. D. Brand: Proving Theorems with the Modification Method. SIAM Journal of Comp., vol 4, No. 4, 1975

    MathSciNet  Google Scholar 

  5. A. Bundy: The Computer Modelling of Mathematical Reasoning. Academic Press, London, 1963

    Google Scholar 

  6. V.J. Digricoli: Resolution by Unification and Equality. Proc. 4th Workshop on Automated Deduction, 1979, Texas

    Google Scholar 

  7. G. Huet, D. Oppen: Equations and Rewrite Rules: A survey. Technical ReportCSL-111, SRI International, 1980

    Google Scholar 

  8. M.C. Harrison, N. Rubin: Another Generalization of Resolution. JACM, vol 25, no. 3, July 1976

    Google Scholar 

  9. G. Huet: Resolution d’equations dans des languages d’ordere l,2,…,ω These d’Etat, Univ. de Paris, VII, 1976

    Google Scholar 

  10. G. Huet: Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems. 16th IEEE Symposium on Foundations of Computer Science, 1977, p. 30–45

    Google Scholar 

  11. J.M. Hullot: A catalogue of canonical Term Rewrite Systems. Technical Report CSL-113, SRI International, 1960

    Google Scholar 

  12. D. Knuth, P. Bendix: Simple Word Problems in Universal Algebras, in: Computational Problems in Abstract Algebra. Ed. Leech I., Pergamon Press, 1970, p. 263–297

    Google Scholar 

  13. Karl Mark G. Raph: The Markgraf Karl Refutation Procedure. Interner Bericht, Memo-Seki-MK-84-01, Fachbereich Informatik, Universität Kaiserslautern, 1964

    Google Scholar 

  14. R. Kowalski: A Proof Procedure Using Connection Graphs. JACM 22, 4, 1975

    Article  Google Scholar 

  15. Y. Lim, L.J. Henschen: A New Hyperparamodulation Strategy for the Equality Relation. Proc. IJCAI-85, Los Angeles, 1985

    Google Scholar 

  16. D. Loveland: Automated Theorem Proving: A logical Basis. North Holland, 1978

    MATH  Google Scholar 

  17. E.L. Lusk, R.A. Overbeek: A Short Problem Set for Testing Systems That Include Equality Reasoning. Argonne National Laboratory, Argonne, Illinois 60439

    Google Scholar 

  18. J. B. Morris: E-resolution: An Extension of Resolution to include the Equality Relation. Proc. IJCAI, 1969, 287–294

    Google Scholar 

  19. G. Plotkin: Building in Equational Theories. Machine Intelligence, vol. 7,1972.

    Google Scholar 

  20. D. Plaisted: Theorem Proving with Abstraction. Artifical Intelligence 16 (1981), p. 47–106

    Article  MathSciNet  MATH  Google Scholar 

  21. G. Robinson, L. Wos: Paramodulation and TP in first order theories with equality. Machine Intelligence 4, 135–150

    Google Scholar 

  22. R.E. Shostak: Refutation Graphs. Artifical Intelligence 7 (1976), p. 51–64

    Article  MathSciNet  MATH  Google Scholar 

  23. R.E. Shostak: An Algorithm for Reasoning About Equality. CACM, July 1976, vol 21, no. 7

    Google Scholar 

  24. E.E. Sibert A machine-oriented Logic incorporating the Equality Axiom. Machine Intelligence, vol 4,1969,103–133

    MathSciNet  MATH  Google Scholar 

  25. J. Siekmann: Universal Unification. Proc. of Conf. on Autom. Deduction, 1954, Napa, USA, Springer Lecture Notes comp. Sci., vol. 170

    Google Scholar 

  26. J. Siekmann, P. Szabo: Universal Unification and Regular ACFM Theories. Proc. IJCAI-51, Vancouver, 1961

    Google Scholar 

  27. J. Siekmann, G. Wrigthson: Pararnodulated Connectiongraphs. Acta Informatica, 1979

    Google Scholar 

  28. L. Wos, G. Robinson, D. Carson, L. Shalla: The Concept of Demodulation in Theorem Proving. J. ACM 14 (October 1967), p. 698–709

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität Kaiserslautern, Postfach 3049, 6750, Kaiserslautern, Deutschland

    Karl-Hans Bläsius

Authors
  1. Karl-Hans Bläsius
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Editor information

Editors and Affiliations

  1. Institut für Mathematische Maschinen und Datenverarbeitung VI, Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstraße 3, 8520, Erlangen, Deutschland

    Herbert Stoyan

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© 1986 Springer-Verlag Berlin Heidelberg

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Bläsius, KH. (1986). Equality Reasoning with Equality-paths. In: Stoyan, H. (eds) GWAI-85. Informatik-Fachberichte, vol 118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71145-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-71145-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16451-7

  • Online ISBN: 978-3-642-71145-9

  • eBook Packages: Springer Book Archive

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