Automated Reasoning Building Blocks

  • Christoph WeidenbachEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9360)


There are automated reasoning building blocks shared between the prime calculi for propositional and first-order logic with equality, conflict driven clause learning (CDCL) and superposition, respectively. In this paper I identify these building blocks by a projection of superposition to propositional logic. Underlying both calculi is a partial model assumption guiding ordered resolution inferences that are not redundant.


Propositional Logic Reasonable Strategy Empty Clause Propositional Clause Resolution Inference 
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.
    Alagi, G., Weidenbach, C.: NRCL - a model building approach to the Bernays-Schönfinkel fragment. In: Lutz, C., Ranise, S. (eds.) FroCoS 2015. LNAI, vol. 9322. Springer (2015)Google Scholar
  2. 2.
    Aravantinos, V., Echenim, M., Peltier, N.: A resolution calculus for first-order schemata. Fundamenta Informaticae 125(2), 101–133 (2013)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bachmair, L., Ganzinger, H.: On restrictions of ordered paramodulation with simplification. In: Stickel, M.E. (ed.) CADE-10. LNCS, vol. 449, pp. 427–441. Springer, Heidelberg (1990)Google Scholar
  4. 4.
    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 (2001)Google Scholar
  5. 5.
    Baumgartner, P., Fuchs, A., Tinelli, C.: Lemma Learning in the Model Evolution Calculus. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 572–586. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  6. 6.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds). Handbook of Satisfiability. IOS Press (2009)Google Scholar
  7. 7.
    Davis, M., Logemann, G., Loveland, D.W.: A machine program for theorem-proving. Communications of the ACM 5(7), 394–397 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Ganzinger, H., Korovin, K.: New directions in instantiation-based theorem proving. In: LICS 2003, pp. 55–64. IEEE Computer Society (2003)Google Scholar
  9. 9.
    Ganzinger, H., Meyer, C., Weidenbach, C.: Soft typing for ordered resolution. In: McCune, W. (ed.) CADE-14. LNAI, vol. 1249, pp. 321–335, Townsville, Australia. Springer, Heidelberg (1997)Google Scholar
  10. 10.
    Bayardo Jr., R.J., Schrag, R.: Using CSP look-back techniques to solve exceptionally hard SAT instances. In: Freuder, E.C. (ed.) CP. LNCS, vol. 1118, pp. 46–60. Springer, Heidelberg (1996)Google Scholar
  11. 11.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient SAT solver. In: DAC, pp. 530–535. ACM (2001)Google Scholar
  12. 12.
    Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53, 937–977 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Nieuwenhuis, R., Rubio, A.: Paramodulation-based theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 7, vol. I, pp. 371–443. Elsevier (2001)Google Scholar
  14. 14.
    Piskac, R., de Moura, L.M., Bjørner, N.: Deciding effectively propositional logic using DPLL and substitution sets. Journal of Automated Reasoning 44(4), 401–424 (2010)Google Scholar
  15. 15.
    Robinson, J.A.: A machine-oriented logic based on the resolution principle. Journal of the ACM 12(1), 23–41 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Silva, J.P.M., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: ICCAD, pp. 220–227. IEEE Computer Society Press (1996)Google Scholar
  17. 17.
    Smullyan, R.M.: First-Order Logic. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer (1968) (revised republication 1995 by Dover Publications)Google Scholar
  18. 18.
    Teucke, A., Weidenbach, C.: First-order logic theorem proving and model building via approximation and instantiation. In: Lutz, C., Ranise, S. (eds) FroCos 2015. LNAI, vol. 9322. Springer (2015)Google Scholar
  19. 19.
    Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson, A., Voronkov, A. (eds) Handbook of Automated Reasoning, ch. 27, vol. 2, pp. 1965–2012. Elsevier (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany

Personalised recommendations