fCube: An Efficient Prover for Intuitionistic Propositional Logic

  • Mauro Ferrari
  • Camillo Fiorentini
  • Guido Fiorino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


We present fCube, a theorem prover for Intuitionistic propositional logic based on a tableau calculus. The main novelty of fCube is that it implements several optimization techniques that allow to prune the search space acting on different aspects of proof-search. We tested the efficiency of our techniques by comparing fCube with other theorem provers. We found that our prover outperforms the other provers on several interesting families of formulas.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Avellone, A., Fiorino, G., Moscato, U.: Optimization techniques for propositional intuitionistic logic and their implementation. Theoretical Computer Science 409(1), 41–58 (2008)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford University Press, Oxford (1997)MATHGoogle Scholar
  3. 3.
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 5, 394–397 (1962)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Ferrari, M., Fiorentini, C., Fiorino, G.: Towards the use of simplification rules in intuitionistic tableaux. In: Gavanelli, M., Riguzzi, F. (eds.) CILC 2009: 24-esimo Convegno Italiano di Logica Computazionale (2009)Google Scholar
  5. 5.
    Hustadt, U., Schmidt, R.A.: Simplification and backjumping in modal tableau. In: de Swart, H. (ed.) TABLEAUX 1998. LNCS (LNAI), vol. 1397, pp. 187–201. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Massacci, F.: Simplification: A general constraint propagation technique for propositional and modal tableaux. In: de Swart, H. (ed.) TABLEAUX 1998. LNCS (LNAI), vol. 1397, pp. 217–231. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    McLaughlin, S., Pfenning, F.: Imogen: Focusing the polarized inverse method for intuitionistic propositional logic. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 174–181. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Raths, T., Otten, J., Kreitz, C.: The ILTP problem library for intuitionistic logic. Journal of Automated Reasoning 31, 261–271 (2007)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Mauro Ferrari
    • 1
  • Camillo Fiorentini
    • 2
  • Guido Fiorino
    • 3
  1. 1.DICOM, Univ. degli Studi dell’InsubriaVareseItaly
  2. 2.DSI, Univ. degli Studi di MilanoMilanoItaly
  3. 3.DIMEQUANT, Univ. degli Studi di Milano-BicoccaMilanoItaly

Personalised recommendations