Skip to main content
SpringerLink
Log in

What Is Negation as Failure?

  • Chapter
Logic Programs, Norms and Action

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7360))

Abstract

An equational approach is used to give semantics to negation as failure. We offer an Equational Calculus and in it we define a new completion for programs with negation as failure in the body of clauses. This approach is compared with other approaches in the literature and a connection is established with argumentation theory.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gabbay, D.: What is negation as failure? (1985) (manuscript)

    Google Scholar 

  2. Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)

    Book  MATH  Google Scholar 

  3. Clark, K.: Negation as failure (Originally published in 1978); reproduced in Readings in nonmonotonic reasoning, pp. 311–325. Morgan Kaufmann Publishers (1987)

    Google Scholar 

  4. Gabbay, D.: An Equational Approach to Argumentation Networks, p. 107 (February 2011); to appear in Argumentation and Computation

    Google Scholar 

  5. Gabbay, D.M.: Introducing Equational Semantics for Argumentation Networks. In: Liu, W. (ed.) ECSQARU 2011. LNCS(LNAI), vol. 6717, pp. 19–35. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Gabbay, D., Reyle, U.: N-Prolog: An Extension of Prolog with Hypothetical Implications I. Journal of Logic Programming 1, 319–355 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gabbay, D.M., Sergot, M.: Negation as inconsistency. Journal of Logic Programming 4(3), 1–35 (1986)

    Article  MathSciNet  Google Scholar 

  8. Gabbay, D.: Modal Provability Interpretation for Negation by Failure. In: Schroeder-Heister, P. (ed.) ELP 1989. LNCS, vol. 475, pp. 179–222. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  9. Miller, D.: A Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network in Computational Logic 2(2), 63–67 (1995)

    Google Scholar 

  10. Cerrito, S.: A linear axiomatization of negation as failure. Journal of Logic Programming 12, 1–24 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cerrito, S.: Negation and linear completion. In: Farinas del Cerro, L., Penttonen, M. (eds.) Intensional Logic for Programming, pp. 155–194. Clarendon Press (1992)

    Google Scholar 

  12. Fitting, M.: Kripke–Kleene semantics for logic programs. Journal of Logic Programming 2, 295–312 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fitting, M.: Negation As Refutation. In: Parikh, R. (ed.) Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pp. 63–70. IEEE (1978)

    Google Scholar 

  14. Kunen, K.: Negation in logic programming. Journal of Logic Programming 4, 289–308 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  15. Giordano, L., Olivetti, N.: Negation as failure in intuitionistic logic programming. In: Proceedings of JICSLP, pp. 431–445 (1992)

    Google Scholar 

  16. Harland, J.: A Kripke-like model for negation as failure. In: Proceedings of the North American Conference on Logic Programming (NACLP), Cleveland, Ohio, October 16-20, pp. 626–642 (1989)

    Google Scholar 

  17. Bonner, A.J., McCarty, L.T.: Adding Negation-as-Failure to Intuitionistic Logic Programming. Technical report, Department of Computer Science,Rutgers University, New Brunswick, NJ 08903 (1990)

    Google Scholar 

  18. Vauzeilles, J.: Negation as Failure and Intuitionistic Three-Valued Logic. In: Jorrand, P., Kelemen, J. (eds.) FAIR 1991. LNCS, vol. 535, pp. 228–241. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  19. Balbiani, P.: Modal logic and negation as failure. J. Logic Computation 11, 331–356 (1991)

    Article  MathSciNet  Google Scholar 

  20. Mobasher, B., Leszczylowski, J., Slutzki, G., Pigozzi, D.: Negation as Partial Failure. In: LPNMR, pp. 244–262 (1993)

    Google Scholar 

  21. Staerk, R.: A Transformation of Propositional Prolog Programs into Classical Logic. In: Marek, V.W., Truszczyński, M., Nerode, A. (eds.) LPNMR 1995. LNCS, vol. 928, pp. 302–315. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  22. Staerk, R.: Cut property and negation as failure. International Journal of Foundations of Computer Science (IJFCS) 5(2), 129–164 (1994)

    Article  MATH  Google Scholar 

  23. Staerk, R.: A complete axiomatization of the three-valued completion of logic programs. J. of Logic and Computation 1(6), 811–834 (1991)

    Article  MATH  Google Scholar 

  24. Shepherdson, J.C.: Negation as failure 2. The Journal of Logic Programming 2(3), 185–202 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  25. Shepherdson, J.C.: Negation as failure: a comparison of Clark’s completed data base and Reiter’s closed world assumption. The Journal of Logic Programming 1(1), 51–79 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  26. Gabbay, D.: N-Prolog: An Extension of Prolog with Hypothetical Implications 2. Journal of Logic Programming 2, 251–283 (1986)

    Article  MathSciNet  Google Scholar 

  27. Olivetti, N., Terracini, L.: N-Prolog and Equivalence of Logic Programs. Journal of Logic, Language and Information 1(4) (1992)

    Google Scholar 

  28. Apt, K.R.,, R.: N Bol. Logic programming and negation: A Survey. J. Logic Programming 19(20), 9–72 (1994)

    Google Scholar 

  29. Gabbay, D.: Modal Provability Foundations for Argumentation Networks. Studia Logica 93(2-3), 181–198 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. Mints, G.: Complete Calculus for Pure Prolog. Proc. Acad. Sci. Estonian SSR 35, 367–380 (1986) (in Russian)

    MathSciNet  MATH  Google Scholar 

  31. Shepherdson, J.C.: A Sound and Complete Semantics for a Version of Negation as Failure. Theoret. Comput. Sci. 65(3), 343–371 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  32. Shepherdson, J.C., Mints, G.: Type Calculi for Logic Programming, Report PM-88-01, School of Mathematics, Univ. of Bristol (1988)

    Google Scholar 

  33. Apt, K.R., van Emden, M.H.: Contributions to the Theory of Logic Programming. J. Assoc. Comput. Much. 29, 841–862 (1982)

    Article  MATH  Google Scholar 

  34. Caminada, M., Gabbay, D.: A logical account of formal argumentation. Studia Logica 93(2-3), 109–145 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. Rahwan, I., Simari, G.R.: Argumentation in Artificial Intelligence. Springer, Heidelberg (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bar Ilan University, Israel

    Dov M. Gabbay

  2. King’s College, London, UK

    Dov M. Gabbay

  3. University of Luxembourg, Luxembourg

    Dov M. Gabbay

Authors
  1. Dov M. Gabbay
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Software and Knowledge Engineering Laboratory, Institute of Informatics and Telecommunications, National Centre for Scientific Research ’Demokritos’, 15310, Athens, Greece

    Alexander Artikis

  2. Department of Computing, Imperial College London, 180 Queen’s Gate, SW7 2AZ, London, UK

    Robert Craven

  3. Department of Computer Engineering, Middle East Technical University, Dumlupınar Bulvarı No. 1, 06800, Çankaya, Ankara, Turkey

    Nihan Kesim Çiçekli

  4. Axiomatics AB, Box 2157, 103 14, Stockholm, Sweden

    Babak Sadighi

  5. Royal Holloway, University of London, UK

    Kostas Stathis

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gabbay, D.M. (2012). What Is Negation as Failure?. In: Artikis, A., Craven, R., Kesim Çiçekli, N., Sadighi, B., Stathis, K. (eds) Logic Programs, Norms and Action. Lecture Notes in Computer Science(), vol 7360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29414-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29414-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29413-6

  • Online ISBN: 978-3-642-29414-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation