Saturation Up to Redundancy for Tableau and Sequent Calculi

  • Martin Giese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)


We discuss an adaptation of the technique of saturation up to redundancy, as introduced by Bachmair and Ganzinger [1], to tableau and sequent calculi for classical first-order logic. This technique can be used to easily show the completeness of optimized calculi that contain destructive rules e.g. for simplification, rewriting with equalities, etc., which is not easily done with a standard Hintikka-style completeness proof. The notions are first introduced for Smullyan-style ground tableaux, and then extended to constrained formula free-variable tableaux.


Free Variable Sequent Calculus Ground Term Main Formula Close Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 2, vol. I, pp. 19–99. Elsevier Science B.V., Amsterdam (2001)CrossRefGoogle Scholar
  2. 2.
    Bachmair, L., Ganzinger, H., Lynch, C., Snyder, W.: Basic paramodulation. Information and Computation 121(2), 172–192 (1995)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cantone, D., Zarba, C.G.: A tableau calculus for integrating first-order reasoning with elementary set theory reasoning. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS, vol. 1847, pp. 143–159. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. 4.
    Fitting, M.C.: First-Order Logic and Automated Theorem Proving, 2nd edn. Springer, Heidelberg (1996)MATHGoogle Scholar
  5. 5.
    Giese, M.: A model generation style completeness proof for constraint tableaux with superposition. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS, vol. 2381, pp. 130–144. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Giese, M.: Simplification rules for constrained formula tableaux. In: Cialdea Mayer, M., Pirri, F. (eds.) TABLEAUX 2003. LNCS, vol. 2796, pp. 65–80. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Giese, M.: A calculus for type predicates and type coercion. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 123–137. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Smullyan, R.M.: First-Order Logic. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 43. Springer, Heidelberg (1968)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Giese
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsLinzAustria

Personalised recommendations