Journal of Automated Reasoning

, Volume 10, Issue 2, pp 265–281 | Cite as

Gentzen-type systems, resolution and tableaux

  • Arnon Avron
Article

Abstract

We show that both the tableaux and the resolution methods can be understood as attempts to exploit the power of cut-elimination theorems in Gentzen-type calculi. Another, related goal is to provide a purely syntactic basis for both methods (in contrast to the semantic proofs concerning resolution that can be found in the textbooks). This allows the use of a fruitful combination of the methods and might be helpful in generalizing them to other logics.

Key words

Resolution tableaux cut-elimination 

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References

  1. 1.
    Avron, A., ‘Simple consequence relations’,Information and Computation 92, 105–139 (1991).Google Scholar
  2. 2.
    Bibel, W.,Automated Theorem Proving, Vieweg Verlag, Braunschweig (1982).Google Scholar
  3. 3.
    Bell, J. L. and Machover, M.,A Course in Mathematical Logic, North-Holland, Amsterdam (1977).Google Scholar
  4. 4.
    Bundy, A.,The Computer Modelling of Mathematical Reasoning, Academic Press, New York (1983).Google Scholar
  5. 5.
    Chang, C. and Lee, R. C.,Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York (1973).Google Scholar
  6. 6.
    Fitting, M. C.,First Order Logic and Automated Theorem Proving, Springer-Verlag, New York (1989).Google Scholar
  7. 7.
    Gallier, J. H.,Logic and Computer Science — Foundations of Automatic Theorem Proving, Harper & Row, New York (1986).Google Scholar
  8. 8.
    Gentzen, G., ‘Investigations into logical deduction’, inThe Collected Work of Gerhard Gentzen, M.E. Szabo (Ed.), North Holland, Amsterdam (1969).Google Scholar
  9. 9.
    Girard, J. Y., Lafont, Y. and Taylor, P.,Proofs and Types, Cambridge University Press, Cambridge (1989).Google Scholar
  10. 10.
    Girard, J. Y.,Proof Theory and Logical Complexity, Bibliopolis (1987).Google Scholar
  11. 11.
    Kowalski, R.,Logic for Problem Solving, Elsevier/North-Holland, New York (1979).Google Scholar
  12. 12.
    Loveland, D. W.,Automated Theorem Proving: A Logical Basis, Elsevier/North-Holland, New York (1978).Google Scholar
  13. 13.
    Oppacher, F. and Suen, E., ‘Controlling deduction with proof condensation and heuristics’, inProceedings of CADE 8, pp. 364–393, Springer-Verlag, Berlin (1986).Google Scholar
  14. 14.
    Robinson, J. A.,Logic: Form and Function, Elsevier/North-Holland, New York (1979).Google Scholar
  15. 15.
    Smullyan, R. M.,First-Order Logic, Springer-Verlag, Berlin (1986).Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Arnon Avron
    • 1
  1. 1.Computer Science Department, Raymond and Beverly Sackler, Faculty of Exact-SciencesTel Aviv UniversityTel AvivIsrael

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