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Between constructive mathematics and PROLOG

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References

  1. Beeson, M.J.: Foundations of constructive mathematics. Berlin: Springer 1985

    Google Scholar 

  2. Blair, H.A.: Decidability in Herbrand bases. In: Minker, J. (ed.) Proceedings Workshop Foundations of Deductive Databases and Logic Programming, Washington, CD, 1986 (draft)

  3. Bruce, K., Meyer, A., Mitchell, J.: The semantics of second order lambda calculus. Inf. Control (to appear)

  4. Buchholz, W., Feferman, S., Pohlers, W., Sieg, W.: Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies. (Lect. Notes Math. Vol. 897) Berlin: Springer 1981

    Google Scholar 

  5. Cardelli, L., Wegner, P.: On understanding types, data abstraction and polymorphism. Comput. Surv.17, 471–522 (1985)

    Google Scholar 

  6. Clark, K.L.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases. New York: Plenum Press 1978, pp. 293–322

    Google Scholar 

  7. Constable, R.L., Allen, S.F., Bromley, H.M., Cleaveland, W.R., Cremer, J.F., Harper, R.W., Howe, D.J., Knoblock, T.B., Mendler, N.P., Panangaden, P., Sasaki, J.T., Smith, S.F.: Implementing mathematics with theNuprl proof development system. Englewood Cliffs: Prentice-Hall 1986

    Google Scholar 

  8. Coquand, T., Huet, G.: Constructions: a higher order proof system for mechanizing mathematics. In: Proceedings EUROCAL 85. (Lect. Notes Comput. Sci., Vol. 203, pp. 151–184) Berlin: Springer 1985

    Google Scholar 

  9. de Bruijn, N.G.: A survey of AUTOMATH. In: Seldin, J.P., Hindley, J.R. (eds.) To H.B. Curry: Essays on combinatory logic, lambda calculus and formalism. New York: Academic Press 1980, pp. 579–606

    Google Scholar 

  10. Dijkstra, E.W.: A new science, from birth to maturity. In: Bauer, F.L., Dijkstra, E.W.: Zwanzig Jahre Institut für Informatik. Report No. 95, Institut für Informatik, ETH Zürich, Zürich, 1988

    Google Scholar 

  11. Gordon, M., Milner, R., Wadsworth, C.: EdinburghLCF. (Lect. Notes Comput. Sci., Vol. 78) Berlin: Springer 1979

    Google Scholar 

  12. Feferman, S.: A language and axiom for explicit mathematics. In: Algebra and Logic. (Lect. Notes Math., Vol. 450, pp. 87–139) Berlin: Springer 1975

    Google Scholar 

  13. Feferman, S.: A theory of variable types. Rev. Colomb. Mat.XIX, 95–105 (1985)

    Google Scholar 

  14. Feferman, S.: Polymorphic typed lambda-calculi in a type-free axiomatic framework. In: Sieg, W. (ed.) Logic and computation (Contemporary mathematics, vol. 106, pp. 101–136) Providence, Rhode Island: American Mathematical Society 1990

    Google Scholar 

  15. Girard, J.-Y.: Une extension de l'interpretation de Gödel a l'analyse, et son application a l'elimination des coupures dans l'analyse et la theorie des types. In: Proceedings 2nd Scandinavian Logic Symposium, pp. 63–92. Amsterdam: North-Holland 1971

    Google Scholar 

  16. Girard, J.-Y.: The systemF of variable types, fifteen years later. Theor. Comput. Sci.45, 159–192 (1986)

    Google Scholar 

  17. Girard, J.-Y.: Proof theory and logical complexity, vol. I. Napoli: Bibliopolis 1987

    Google Scholar 

  18. Hayashi, S., Nakano, H.: PX a computational logic. Report Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 1987

    Google Scholar 

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

    Google Scholar 

  20. Jaffar, J., Stuckey, P.J.: Canonical logic programs. J. Logic Program.2, 143–155 (1986)

    Google Scholar 

  21. Jäger, G.: Some contributions to the logical analysis of circumscription. In: Proceedings of CADE 86—8th International Conference on Automated Deduction. (Lect. Notes Comput. Sci., Vol. 230, pp. 154–171) Berlin: Springer 1986

    Google Scholar 

  22. Jäger, G.: Induction in the elementary theory of types and names. In: Börger, E., Kleine Büning, H., Richter, M.M. (eds.) Proceedings CSL '87. (Lect. Notes Comput. Sci., Vol. 329, pp. 118–128) Berlin: Springer 1988

    Google Scholar 

  23. Jäger, G.: Non-monotonic reasoning by axiomatic extensions. In: Fenstad, J.E., Frolow, I.T., Hilpinen, R.: Proceedings 8th International Congress for Logic, Methodology and Philosophy of Science, pp. 93–110. Amsterdam: North-Holland 1989

    Google Scholar 

  24. Jäger, G., Stärk, R.: The defining power of stratified and hierarchical logic programs. Technical report IAM-90-004, Institut für Informatik und angewandte Mathematik, Universität Bern, 1990

  25. Kunen, K.: Negation in logic programming. J. Logic Program.4, 289–308 (1988)

    Google Scholar 

  26. Kunen, K.: Signed data dependencies in logic programs. J. Logic Program.7, 231–245 (1989)

    Google Scholar 

  27. Lifschitz, V.: Closed world data bases and circumscription. Artif. Intell.27, 229–235 (1985)

    Google Scholar 

  28. Lifschitz, V.: On the satisfiability of circumscription. Artif. Intell.28, 17–27 (1986)

    Google Scholar 

  29. Lloyd, J.W.: Foundations of logic programming. Berlin: Springer 1987

    Google Scholar 

  30. Martin-Löf, P.: Constructive mathematics and computer programming. In: Proceedings 6th International Congress for Logic, Methodology and Philosophy of Science, pp. 153–175. Amsterdam: North-Holland 1982

    Google Scholar 

  31. Martin-Löf, P.: Intuitionistic type theory. Napoli: Bibliopolis 1984

    Google Scholar 

  32. McCarthy, J.: Circumscription — a form of non-monotonic reasoning. Artif. Intell.13, 27–39 (1980)

    Google Scholar 

  33. McCarthy, J.: Applications of circumscription to formalizing common sense knowledge. Artif. Intell.28, 89–118 (1986)

    Google Scholar 

  34. Nordstrom, B., Petersson, K.: Types and specifications. In: Proceedings IFIP '83, pp. 915–920. Amsterdam: North-Holland 1983

    Google Scholar 

  35. Nordstrom, B., Smith, J.: Propositions, types, and specifications in Martin-Löf's type theory. BIT24, (3), 288–301 (1984)

    Google Scholar 

  36. Reiter, R.: On closed world data bases. In: Gallaire, H., Minker, J. (eds.) Logic and data bases, pp. 55–76. New York: Plenum Press 1978

    Google Scholar 

  37. Reynolds, J.C.: Towards a theory of type structure. In: Proceedings Colloque sur la Programmation. (Lect. Notes Comput. Sci., Vol. 19, pp. 408–425) Berlin: Springer 1974

    Google Scholar 

  38. Schütte, K.: Proof theory. Berlin: Springer 1977

    Google Scholar 

  39. Shepherdson, J.C.: Negation in logic programming. In: Minker, J. (ed.) Deductive databases and logic programming, pp. 19–88. Los Altos: Kaufmann 1988

    Google Scholar 

  40. Shepherdson, J.C.: A sound and complete semantics for a version of negation as failure. Theor. Comput. Sci.65, 343–371 (1989)

    Google Scholar 

  41. Takeuti, G.: Proof theory. Amsterdam: North-Holland 1975

    Google Scholar 

  42. Troelstra, A.S., van Dalen, D.: Constructivism in mathematics I, II. Amsterdam: North-Holland 1988

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik und angewandte Mathematik, Universität Bern, Länggassstrasse 51, CH-3012, Bern, Switzerland

    Gerhard Jäger

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  1. Gerhard Jäger
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Dedicated to Professor Kurt Schütte on the occasion of his 80th birthday

A preliminary version of this article has been published in the Proceedings 11th World Computer Congress, IFIP '89

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Jäger, G. Between constructive mathematics and PROLOG. Arch Math Logic 30, 297–310 (1991). https://doi.org/10.1007/BF01621473

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  • DOI: https://doi.org/10.1007/BF01621473

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