On the Complexity of Disjunction and Explicit Definability Properties in Some Intermediate Logics

  • Mauro Ferrari
  • Camillo Fiorentini
  • Guido Fiorino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2514)


In this paper we provide a uniform framework, based on extraction calculi, where to study the complexity of the problem to decide the disjunction and the explicit definability properties for Intuitionistic Logic and some Superintuitionistic Logics. Unlike the previous approaches, our framework is independent of structural properties of the proof systems and it can be applied to Natural Deduction systems, Hilbert style systems and Gentzen sequent systems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Avellone, M. Ferrari, and C. Fiorentini. A formal framework for synthesis and verification of logic programs. In K.-K. Lau, editor, Logic Based Program Synthesis and Transformation, 10th International Workshop, LOPSTR 2000, Selected Papers, volume 2042 of Lecture Notes in Computer Science, pages 1–17. Springer-Verlag, 2001.Google Scholar
  2. 2.
    S. Buss and G. Mints. The complexity of the disjunction and existential properties in intuitionistic logic. Annals of Pure and Applied Logic, 99(3):93–104, 1999.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. Buss and P. Pudlák. On the computational content of intuitionistic propositional proofs. Annals of Pure and Applied Logic, 109(1–2):49–64, 2001.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M. Ferrari. Strongly Constructive Formal Systems. PhD thesis, Dipartimento di Scienze dell’Informazione, Universitá degli Studi di Milano, Italy, 1997. Available at http://homes.dsi.unimi.it/~ferram.Google Scholar
  5. 5.
    M. Ferrari and C. Fiorentini. A proof-theoretical analysis of semiconstructive intermediate theories. Studia Logica, to appear.Google Scholar
  6. 6.
    M. Ferrari, C. Fiorentini, and P. Miglioli. Goal oriented information extraction in uniformly constructive calculi. In Argentinian Workshop on Theoretical Computer Science (WAIT’99), pages 51–63. Sociedad Argentina de Informática e Investigación Operativa, 1999.Google Scholar
  7. 7.
    M. Ferrari, P. Miglioli, and M. Ornaghi. On uniformly constructive and semicon-structive formal systems. Logic Journal of the IGPL, to appear.Google Scholar
  8. 8.
    C. Fiorentini and P. Miglioli. A cut-free sequent calculus for the logic of constant domains with a limited amount of duplications. Logic Journal of the IGPL, 7(6):733–753, 1999.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    D.M. Gabbay. Semantical Investigations in Heyting’s Intuitionistic Logic. Reidel, Dordrecht, 1981.MATHGoogle Scholar
  10. 10.
    S. Görnemann. A logic stronger than intuitionism. Journal of Symbolic Logic, 36:249–261, 1971.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    G. Kreisel and H. Putnam. Eine Unableitbarkeitsbeweismethode für den intuition-istischen Aussagenkalkül. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 3:74–78, 1957.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    P. Miglioli, U. Moscato, and M. Ornaghi. Constructive theories with abstract data types for program synthesis. In D.G. Skordev, editor, Mathematical Logic and its Applications, pages 293–302. Plenum Press, New York, 1987.Google Scholar
  13. 13.
    P. Miglioli, U. Moscato, and M. Ornaghi. Abstract parametric classes and abstract data types defined by classical and constructive logical methods. The Journal of Symbolic Computation, 18(1):41–81, 1994.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    H. Ono. Some results on the intermediate logics. Publications of the Research Institute for Mathematical Sciences, Kyoto University, 8:117–130, 1972.CrossRefGoogle Scholar
  15. 15.
    C.A. Smorynski. Applications of Kripke semantics. In A.S. Troelstra, editor, Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, volume 344 of Lecture Notes in Mathematics, pages 324–391. Springer-Verlag, 1973.Google Scholar
  16. 16.
    A.S. Troelstra, editor. Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, volume 344 of Lecture Notes in Mathematics. Springer-Verlag, 1973.Google Scholar
  17. 17.
    A.S. Troelstra and H. Schwichtenberg. Basic Proof Theory, volume 43 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Mauro Ferrari
    • 1
  • Camillo Fiorentini
    • 1
  • Guido Fiorino
    • 2
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly
  2. 2.CRIIUniversità dell’InsubriaVareseItaly

Personalised recommendations