Computational Logic: Memories of the Past and Challenges for the Future

  • John Alan Robinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1861)


The development of computational logic since the introduction of Frege’s modern logic in 1879 is presented in some detail. The rapid growth of the field and its proliferation into a wide variety of subfields is noted and is attributed to a proliferation of subject matter rather than to a proliferation of logic itself. Logic is stable and universal, and is identified with classical first order logic. Other logics are here considered to be first order theories, syntactically sugared in notationally convenient forms. From this point of view higher order logic is essentially first order set theory. The paper ends by presenting several challenging problems which the computational logic community now faces and whose solution will shape the future of the field.


Logic Program Logic Programming Functional Programming Horn Clause Sequent Calculus 
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.
    Quine, W.V. The Ways of Paradox and Other Essays, Random House, 1966.Google Scholar
  2. 2.
    Gödel, K. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. Princeton, 1940.Google Scholar
  3. 3.
    Hilbert, D. Mathematical Problems. Bulletin of the American Mathematical Society, Volume 8, 1902, pp. 437–479. (Engish translation of original German version).MathSciNetCrossRefGoogle Scholar
  4. 4.
    Heijenoort, J. van (editor). From Frege to Gödel; A source Book in Mathematical Logic, 1879–1931. Harvard, 1967.Google Scholar
  5. 5.
    Tarski, A. Logic, Semantics, Metamathematics. Oxford, 1956.Google Scholar
  6. 6.
    Cohen, P. J. Set Theory and the Continuum Hypothesis. Benjamin, 1966.Google Scholar
  7. 7.
    Davis, M. (editor). The Undecidable. Raven Press, 1965.Google Scholar
  8. 8.
    Siekmann, J. and Wrightson, G. (editors). The Automation of Reasoning: Classical Papers on Computational Logic. 2 Volumes, Springer, 1983.Google Scholar
  9. 9.
    Beth, E. Semantic Entailmentand Formal Derivability, North Holland, 1955.Google Scholar
  10. 10.
    Hintikka, J. Form and Content in Quantification Theory. Acta Philosophica Fennica 8, 1955, pp. 7–55.MathSciNetGoogle Scholar
  11. 11.
    Gentzen, G. Untersuchungen über das logische Schliessen. Mathematische Zeitschrift 39, 1934, pp. 176–210, 405–431.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Boyer, R. S. (editor). Automated Reasoning. Essays in Honor of Woody Bledsoe. Kluwer, 1991.Google Scholar
  13. 13.
    Walker, D. and Norton, L. (editors). Proceedings of the International Joint Conference on Artificial Intelligence, Washington D.C., 1969.Google Scholar
  14. 14.
    Brachman, R. and Levesque, H. (editors). Readings in Knowledge Representation. Morgan Kaufmann, 1985.Google Scholar
  15. 15.
    Colmerauer, A. Curriculum Vitae, January 1999. Private communication.Google Scholar
  16. 16.
    Kowalski, R. and Kuehner, D. Linear Resolution with Selection Function. Artificial Intelligence 2, 1971, pp. 227–260.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Meltzer, B. and Michie, D. Machine Intelligence 7, Edinburgh, 1972.Google Scholar
  18. 18.
    Meltzer, B. and Michie, D. Machine Intelligence 6, Edinburgh, 1971.Google Scholar
  19. 19.
    Warren, D. and Pereira, L. PROLOG: The Language and Its Implementatior Compared with LISP. SIGPLAN Notices 12, No 8, August 1977, pp. 109 ff.CrossRefGoogle Scholar
  20. 20.
    Kowalski, R. Logic for Problem Solving. North Holland, 1979.Google Scholar
  21. 21.
    International Conference on Fifth Generation Computer Systems 1992, Proceedings, ICOT, Tokyo, 1992.Google Scholar
  22. 22.
    The Journal of Logic Programming, 1, 1984.Google Scholar
  23. 23.
    Furukawa, K., Michie, D. and Muggleton, S. Machine Intelligence 15, Oxford University Press, 1999.Google Scholar
  24. 24.
    Apt, K. and Bezem, M. Formulas as Programs. Report PNA-R9809, CWI, Amsterdam, October 1998.Google Scholar
  25. 25.
    Harms, M. A Unified Computation Model for Functional and Logic Programming. 24th Annual SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’97), 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • John Alan Robinson
    • 1
  1. 1.Highland InstituteGreenfieldUSA

Personalised recommendations