Skip to main content
Log in

Proof theory and complexity

  • Published:
Synthese Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Eick, A. and E. Fehr: 1982, ‘Inconsistencies of pure LISP’, in A. B. Cremers and H. P. Kriegel (eds.), Theoretical Computer Science (6th GI-Conference), Springer-Verlag, Berlin, pp. 101–110.

    Google Scholar 

  2. Gandy, R. O.: 1980, ‘Proofs of strong normalization’, in J. P. Seldin and J. R. Hindley (eds.), To H. B. Curry. Essays on combinatory logic, lambda calculus and formalism, Academic Press, London-New York, pp. 457–477.

    Google Scholar 

  3. Garey, M. R. and D. S. Johnson: 1979, Computers and intractability. A guide to the theory of NP-completeness, Freeman and Co., San Francisco.

    Google Scholar 

  4. Girard, J.-Y.: 1984, Proof theory and logical complexity, Bibliopolis, Naples.

    Google Scholar 

  5. Grzegorczyk, A.: 1953, ‘Some classes of recursive functions’, Rozprawy Matematyczne 4, 1–45.

    Google Scholar 

  6. Howard, W.: 1980, ‘The formulae-as-types notion of construction’, in J. P. Seldin and J. R. Hindley (eds.), To H. B. Curry. Essays on combinatory logic, lambda calculus and formalism, Academic Press, London-New York, pp. 479–490.

    Google Scholar 

  7. Kleene, S. C.: 1935, ‘A theory of positive integers in formal logic. I’, American Journal of Mathematics 57, 153–173.

    Google Scholar 

  8. Kolmogorov, A. N.: 1932, ‘Zur Deutung der intuitionistischen Logik’, Mathematische Zeitschrift 35, 58–65.

    Google Scholar 

  9. Minc, G. E.: 1982, ‘Primitive recursive estimate of strong normalization for predicate calculus’, Journal of Soviet Mathematics 20, 2334–2336.

    Google Scholar 

  10. Prawitz, D.: 1965, Natural deduction. A proof-theoretical study, Almqvist & Wiksell, Stockholm.

    Google Scholar 

  11. Prawitz, D.: 1971, ‘Ideas and results in proof theory’, in J. E. Fenstad (ed.), Proceedings of the Second Scandinavian Logic Symposium, North-Holland, Amsterdam, pp. 235–307.

    Google Scholar 

  12. Prawitz, D.: 1981, ‘Validity and normalizability of proofs in 1st and 2nd order classical and intuitionistic logic’, in S. Bernini (ed.), Atti del Congresso Nazionale di Logica, Montecatini Terme 1–5 ottobre 1979, Bibliopolis, Naples, pp. 11–36.

    Google Scholar 

  13. Schwichtenberg, H.: 1982, ‘Complexity of normalization in the pure typed lambdacalculus’, in A. S. Troelstra and D. van Dalen (eds.), The L.E.J. Brouwer Centenary Symposium, North-Holland, Amsterdam, pp. 453–457.

    Google Scholar 

  14. Statman, R.: 1974, Structural complexity of proofs, Dissertation, Stanford University.

  15. Statman, R.: 1978, ‘Bounds for proof-search and speed-up in the predicate calculus’, Annals of Mathematical Logic 15, 225–287.

    Google Scholar 

  16. Statman, R.: 1979, ‘The typed λ-calculus is not elementary recursive’, Theoretical Computer Science 9, 73–81.

    Google Scholar 

  17. Wang, H.: 1981, Popular lectures on mathematical logic, Van Nostrand, New York and Science Press, Beijing.

    Google Scholar 

  18. Zucker, J.: 1974, ‘The correspondence between cut-elimination and normalization’, Annals of Mathematical Logic 7, 1–155.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This is a revised and retitled version of a paper presented to the workshop ‘The present state of the problem of foundations of mathematics' held at the Villa di Mondeggi, 15–19 June 1981.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cellucci, C. Proof theory and complexity. Synthese 62, 173–189 (1985). https://doi.org/10.1007/BF00486045

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00486045

Keywords

Navigation