Skip to main content
SpringerLink
Log in

Abduction with Penalization in Logic Programming

  • Conference paper
  • First Online:
AI*IA 2001: Advances in Artificial Intelligence (AI*IA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2175))

Included in the following conference series:

  • 319 Accesses

Abstract

Abduction, first proposed in the setting of classical logics, has been studied with growing interest in the logic programming area during the last years.

In this paper we study abduction with penalization in logic programming. This form of abductive reasoning, which has not been previously analyzed in logic programming, turns out to represent several relevant problems, including optimization problems, very naturally. We define a formal model for abduction with penalization from logic programs, which extends the abductive framework proposed by Kakas and Mancarella. We show the high expressiveness of this formalism, by encoding a couple of relevant problems, including the well-know Traveling Salesman Problem from optimization theory, in this abductive framework. The resulting encodings are very simple and elegant. We analyze the complexity of the main decisional problems arising in this framework. An interesting result in this course is that “negation comes for free.” Indeed, the addition of (even unstratified) negation does not cause any further increase to the complexity of the abductive reasoning tasks (which remains the same as for not-free programs).

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. C. Baral and M. Gelfond. Logic Programming and Knowledge RepresentationJournal of Logic Programming, 1994.

    Google Scholar 

  2. F. Buccafurri, N. Leone, and P. Rullo. Enhancing Disjunctive Datalog by Constraints. IEEE Transactions on Knowledge and Data Engineering, 12(5):845–860, 2000.

    Article  Google Scholar 

  3. E. Charniak and P. McDermott. Introduction to Artificial Intelligence. Addison Wesley, Menlo Park, Ca, 1985.

    Google Scholar 

  4. L. Console, D. Theseider Dupré, and P. Torasso. On the Relationship Between Abduction and Deduction. Journal of Logic and Computation, 1(5):661–690, 1991.

    Article  MathSciNet  Google Scholar 

  5. M. Denecker and D. De Schreye. Representing incomplete knowledge in abductive logic programming. In Proc. of the International Symposium on Logic Programming, pp. 147–163, 1993.

    Google Scholar 

  6. P. Dung. Negation as Hypotheses: An Abductive Foundation for Logic Programming. In Proceedings ICLP-91. MIT Press, 1991.

    Google Scholar 

  7. Eiter, T., Gottlob, G.. The Complexity of Logic-Based Abduction. Journal of the ACM, 42(1):3–42, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. Eiter, T., Gottlob, G., and Mannila, H.. Disjunctive Datalog. ACM Transactions on Database Systems, 22(3):364–418, 1997.

    Article  Google Scholar 

  9. Eiter, T., Gottlob, G., and Leone, N.. Abduction from Logic Programs: Semantics and Complexity. Theoretical Computer Science, 189(1–2): 129–177, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  10. T. Eiter, W. Faber, N. Leone, and G. Pfeifer. Declarative Problem-Solving Using the DLV System. Logic-Based Artificial Intelligence. Kluwer Academic Publishers, 2000.

    Google Scholar 

  11. M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In Proc. Fifth Logic Programming Symposium, pp. 1070–1080. MIT Press, 1988.

    Google Scholar 

  12. J. R. Hobbs and M. E. Stickel. Interpretation as Abduction. In Proc. 26th Annual Meeting of the Assoc. for Computational Linguistics, 1988.

    Google Scholar 

  13. A. Kakas and R. Kowalski and F. Toni. Abductive Logic Programming. Journal of Logic and Computation, 2(6):719–771, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Kakas and P. Mancarella. Generalized Stable Models: a Semantics for Abduction. In Proc. of ECAI-90, pp. 385–391, 1990.

    Google Scholar 

  15. A. Kakas and P. Mancarella. Database Updates Through Abduction. In Proceedings VLDB-90, pp. 650–661, 1990.

    Google Scholar 

  16. K. Konolige. Abduction versus closure in causal theories. Artificial Intelligence, 53:255–272, 1992.

    Article  MathSciNet  Google Scholar 

  17. Papadimitriou, C.. The Complexity of Unique Solutions. Journal of the ACM 31, 492–500, 1984.

    Article  Google Scholar 

  18. C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

    Google Scholar 

  19. C. S. Peirce. Abduction and induction. In J. Buchler, editor, Philosophical Writings of Peirce, chapter 11. Dover, New York, 1955.

    Google Scholar 

  20. D. Poole. Normality and Faults in Logic Based Diagnosis. In Proceedings IJCAI-89, pp. 1304–1310, 1989.

    Google Scholar 

  21. C. Sakama and K. Inoue. On the Equivalence between Disjunctive and Abductive Logic Programs. In Proc. of ICLP-94, pp. 88–100, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Calabria, I-87030, Rende (CS), Italy

    Nicola Leone & Simona Perri

  2. D.E.I.S., University of Calabria, 87030, Rende (CS), Italy

    Francesco Scarcello

Authors
  1. Nicola Leone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Simona Perri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francesco Scarcello
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Bari, via Orabona 4, 70125, Bari, Italy

    Floriana Esposito

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Leone, N., Perri, S., Scarcello, F. (2001). Abduction with Penalization in Logic Programming. In: Esposito, F. (eds) AI*IA 2001: Advances in Artificial Intelligence. AI*IA 2001. Lecture Notes in Computer Science(), vol 2175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45411-X_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-45411-X_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42601-1

  • Online ISBN: 978-3-540-45411-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation