Skip to main content
SpringerLink
Log in

Relating Defeasible Logic to Extended Logic Programs

  • Conference paper
  • First Online:
Methods and Applications of Artificial Intelligence (SETN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2308))

Included in the following conference series:

Abstract

Defeasible reasoning is a simple but e.cient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches.

In this paper we establish close links to known semantics of extended logic programs. In particular, we give a translation of a defeasible theory D into a program P(D). We show that under a condition of decisiveness, the defeasible consequences of D correspond exactly to the sceptical conclusions of P(D) under the answer set semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of D are included in all answer sets of P(D)). If we wish a complete embedding for the general case, we need to use the Kunen semantics of P(D), instead.

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. G. Antoniou, D. Billington and M.J. Maher. On the analysis of regulations using defeasible rules. In Proc. 32nd Hawaii International Conference on Systems Science, 1999.

    Google Scholar 

  2. G. Antoniou, D. Billington and M. Maher. Defeasible Logic versus Logic Programming without Negation as Failure. Journal of Logic Programming 41,1 (2000): 45–57.

    MathSciNet  Google Scholar 

  3. G. Antoniou, M.J. Maher and D. Billington. Defeasible Logic versus Logic Programming without Negation as Failure, Journal of Logic Programming, 42 (2000): 47–57.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Antoniou, D. Billington, G. Governatori and M.J. Maher. A flexible framework for defeasible logics. In Proc. 17th American National Conference on Artificial Intelligence (AAAI-2000), 405–410.

    Google Scholar 

  5. G. Antoniou, D. Billington, G. Governatori and M.J. Maher. Representation results for defeasible logic. ACM Transactions on Computational Logic 2 (2001): 255–287

    Article  MathSciNet  Google Scholar 

  6. D. Billington. Defeasible Logic is Stable. Journal of Logic and Computation 3 (1993): 370–400.

    Article  MathSciNet  Google Scholar 

  7. J.P. Delgrande, T Schaub and H. Tompits. Logic Programs with Compiled Preferences. In Proc. ECAI’2000, 464–468.

    Google Scholar 

  8. M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proc. International Conference on Logic Programming, MIT Press 1988, 1070–1080.

    Google Scholar 

  9. M. Gelfond and V. Lifschitz. Classical negation in logic programs and deductive databases. New Generation Computing 9 (1991): 365–385.

    Article  Google Scholar 

  10. G. Governatori, A. ter Hofstede and P. Oaks. Defeasible Logic for Automated Negotiation. In Proc. Fifth CollECTeR Conference on Electronic Commerce, Brisbane 2000.

    Google Scholar 

  11. B.N. Grosof. Prioritized conflict handling for logic programs. In Proc. International Logic Programming Symposium, MIT Press 1997, 197–211.

    Google Scholar 

  12. B.N. Grosof, Y. Labrou and H.Y. Chan. A Declarative Approach to Business Rules in Contracts: Courteous Logic Programs in XML. In Proc. 1st ACM Conference on Electronic Commerce (EC-99), ACM Press 1999.

    Google Scholar 

  13. H.A. Kautz and B. Selman. Hard problems for simple default theories. Artificial Intelligence 28 (1991): 243–279.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. M.J. Maher, A. Rock, G. Antoniou, D. Billington and T. Miller. Efficient Defeasible Reasoning Systems. In Proc. 12th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2000), IEEE 2000, 384–392.

    Google Scholar 

  16. M.J. Maher. A Denotational Semantics for Defeasible Logic. In Proc. First International Conference on Computational Logic, LNAI1861, Springer, 2000, 209–222.

    Google Scholar 

  17. M.J. Maher. Propositional Defeasible Logic has Linear Complexity. Theory and Practice of Logic Programming, to appear.

    Google Scholar 

  18. V. Marek and M. Truszczynski. Nonmonotonic Logic. Springer 1993.

    Google Scholar 

  19. L. Morgenstern. Inheritance Comes of Age: Applying Nonmonotonic Techniques to Problems in Industry. ArtiFIcial Intelligence, 103 (1998): 1–34.

    Article  MathSciNet  Google Scholar 

  20. D. Nute. Defeasible Logic. In D.M. Gabbay, C.J. Hogger and J.A. Robinson (eds.): Handbook of Logic in Artificial Intelligence and Logic Programming Vol. 3, Oxford University Press 1994, 353–395.

    Google Scholar 

  21. H. Prakken. Logical Tools for Modelling Legal Argument: A Study of Defeasible Reasoning in Law. Kluwer Academic Publishers 1997.

    Google Scholar 

  22. D.M. Reeves, B.N. Grosof, M.P. Wellman, and H.Y. Chan. Towards a Declarative Language for Negotiating Executable Contracts, Proceedings of the AAAI-99 Workshop on Artificial Intelligence in Electronic Commerce (AIEC-99), AAAI Press / MIT Press, 1999.

    Google Scholar 

  23. R. Reiter. A Logic for Default Reasoning. Artificial Intelligence 13(1980): 81–132.

    Article  MATH  MathSciNet  Google Scholar 

  24. D.D. Touretzky, J.F. Horty and R.H. Thomason. A Clash of Intuitions: The Current State of Nonmonotonic Multiple Inheritance Systems. In Proc. IJCAI-87, Morgan Kaufmann 1987, 476–482.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Bremen, Germany

    George Antoniou

Authors
  1. George Antoniou
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Informatics, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece

    Ioannis P. Vlahavas

  2. N.C.S.R. “Demokritos”, Inst. of Informatics & Telecommunications Software and Knowledge Engineering Lab, 15310, Aghia Paraskevi, Greece

    Constantine D. Spyropoulos

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Antoniou, G. (2002). Relating Defeasible Logic to Extended Logic Programs. In: Vlahavas, I.P., Spyropoulos, C.D. (eds) Methods and Applications of Artificial Intelligence. SETN 2002. Lecture Notes in Computer Science(), vol 2308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46014-4_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-46014-4_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43472-6

  • Online ISBN: 978-3-540-46014-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation