Skip to main content
SpringerLink
Log in

Foundation of logic programming based on inductive definition

  • Regular Papers
  • Published:
New Generation Computing Aims and scope Submit manuscript

Abstract

A logical system of inference rules intended to give the foundation of logic programs is presented. The distinguished point of the approach taken here is the application of the theory of inductive definitions, which allows us to uniformly treat various kinds of induction schema and also allows us to regardnegation as failure as a kind of induction schema. This approach corresponds to the so-called least fixpoint semantics. Moreover, in our formalism, logic programs are extended so that a condition of a clause may be any first-order formula. This makes it possible to write a quantified specification as a logic program. It also makes the class of induction schemata much larger to include the usual course-of-values inductions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Andrew, P. B.: “Transforming matings into natural deduction proofs”, 5th Conference on Automated Deduction, Lecture Notes in Computer Science,87 (Springer-Verlag, 1980) 281–292.

  2. Apt, R. K. and van Emden, M. H.: “Contributions to the theory of logic programming”, J.ACM,29, No. 3 (July, 1982) 841–862.

    Article  MATH  Google Scholar 

  3. Bibel, W.: “A syntactic connection between proof procedures and refutation procedures”, Theoretical Computer Science 3rd GI Conference, Lecture Notes in Computer Science,48 (Springer-Verlag, 1978) 215–224.

    MathSciNet  Google Scholar 

  4. Bowen, K. A.: “Programming with full first-order logic”, Machine Intelligence,10 (1982) 421–440.

    Google Scholar 

  5. Clark, K. L.: “Negation as failure”, Logic and Data Bases (ed. H. Gallaire and J. Miker) (Plenum Press, New York, 1978) 293–324.

    Google Scholar 

  6. Clark, K. L.: “Predicate logic as a computational formalism”, Research Monograph:79/59 TOC (Imperial College, 1979).

  7. Clark, K. L. and Darlington, J.: “Algorithmic classification through synthesis”, Comput. J.,23, No. 1 (1980) 61–65.

    Article  MATH  MathSciNet  Google Scholar 

  8. Clark, K. L. and Tärnlund, S-Å.: “A first order theory of data and programs”, Proc. IFIP-77 Congress (North-Holland, 1977) 937–944.

  9. Hagiya, M.: “Logic programming and inductive definition”, Preprint420 (Research Institute for Mathematical Science, Kyoto University, 1983).

  10. Hansson, Å. and Tärnlund, S-Å.: “A natural programming calculus”, Proc. 6th Int. Joint Conf. on Artificial Intelligence (1979) 348–355.

  11. Kowalski, R. A.: “Predicate logic as a programming language”, Information Processing,74 (ed. Rosenfeld, J.) (North-Holland, 1974) 569–574.

    Google Scholar 

  12. Martin-Löf, P.: “Hauptsatz for the intuitionistic theory of iterated inductive definitions”, Proc. Second Scandinavian Logic Symposium (North-Holland, Amsterdam, 1970) 179–216.

    Google Scholar 

  13. McCarthy, J.: “Circumscription—A form of non-monotonic reasoning”, Artificial Intelligence,13 (1980) 27–39.

    Article  MATH  MathSciNet  Google Scholar 

  14. Prawitz, D.: Natural deduction (Almquist and Wksell, Stockholm, 1965).

    MATH  Google Scholar 

  15. Prawitz, D.: “Ideas and results in proof theory”, Proc. Second Scandinavian Logic Symposium (North-Holland, Amsterdam, 1970) 235–307.

    Google Scholar 

  16. Sakurai, T.: “Prolog and inductive definition”, Techinical Report,83-10 (University of Tokyo, 1983).

  17. Sato, T.: “Negation and semantics of Prolog programs”, Proc. First Int. Logic Programming Conf. (1982) 169–174.

Download references

Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, 606, Kyoto, Japan

    Masami Hagiya

  2. Department of Information Science, Faculty of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113, Tokyo, Japan

    Takafumi Sakurai

Authors
  1. Masami Hagiya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takafumi Sakurai
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Hagiya, M., Sakurai, T. Foundation of logic programming based on inductive definition. NGCO 2, 59–77 (1984). https://doi.org/10.1007/BF03037052

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03037052

Keywords

Search

Navigation