Skip to main content
SpringerLink
Log in

Computing Equilibrium Models Using Signed Formulas

  • Conference paper
  • First Online:
Computational Logic — CL 2000 (CL 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1861))

Included in the following conference series:

Abstract

We discuss equilibrium logic, first presented in Pearce (1997), as a system of nonmonotonic reasoning based on the nonclassical logic N 5 of here-and-there with strong negation. Equilibrium logic is a conservative extension of answer set inference, not only for extended, disjunctive logic programs, but also for significant extensions such as the programs with nested expressions described by Lifschitz, Tang and Turner (forthcoming). It provides a theoretical basis for extending the paradigm of answer set programming beyond current systems such as smodels and dlv. The paper provides proof systems for N 5 and for model-checking in equilibrium logic. The reduction of the latter problem to an unsatisfiability problem of classical logic yields complexity results for the various decision problems concerning equilibrium entailment. The reduction also yields a basis for the practical implementation of an automated reasoning tool.

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. Aguilera, G, P. de Guzmán, I, Ojeda-Aciego, M and Valverde, A. Reductions for non-clausal theorem proving. Theoretical Computer Science (2000). To appear.

    Google Scholar 

  2. Alferes, J J, Leite, J A, Pereira, L M, Przymusinska, H, and Przymusinski, T C, Dynamic Logic Programming, in A. Cohn, L. Schubert and S. Shapiro (eds.), Procs. KR’98, Morgan Kaufmann, 1998.

    Google Scholar 

  3. Egly, U, Eiter, T, Tompits, H and Woltran, S, Implementing Default reasoning Using Quantified Boolean Formulae (System Description), in F Bry, U Geske and D Sepiel (eds), Proc 14. Workshop Logische Programmierung, GMD Report 90, Jan 2000.

    Google Scholar 

  4. Eiter, T, Leone N, Mateis, C, Pfeifer, G and Scarcello, F, A Deductive System for Nonmonotonic Reasoning, in Proc. LPNMR97, Springer, 1997.

    Google Scholar 

  5. Eiter, T, Leone N, Mateis, C, Pfeifer, G and Scarcello, F, The KR System dlv: Progress Report, Comparisons and Benchmarks, in Proc. KR98, Morgan Kaufmann, 1998

    Google Scholar 

  6. Gelfond, M, and Lifschitz, V, The Stable Model Semantics for Logic Programs, in K Bowen and R Kowalski (eds), Proc 5th ICLP, MIT Press, 1070–1080.

    Google Scholar 

  7. Gelfond, M and Lifschitz, V, Logic Programs with Classical Negation, in D Warren and P Szeredi (eds), Proc ICLP-90, MIT Press, 1990, 579–597.

    Google Scholar 

  8. Gelfond, M, and Lifschitz, V, Classical Negation in Logic Programs and Disjunctive Databases, New Generation Computing (1991), 365–387.

    Google Scholar 

  9. Greco, S, Leone, N, Scarcello, F, DATALOG with Nested Rules, in Proc. (LPKR’ 97), Port Jefferson, New York, LNAI 1471, pp. 52–65, Springer, 1998.

    Google Scholar 

  10. Gurevich, Y, Intuitionistic Logic with Strong Negation, Studia Logica 36 (1977).

    Google Scholar 

  11. P. de Guzmán, I., Ojeda-Aciego, M. and Valverde, A. Multiple-Valued Tableaux with Δ-reductions. In Proc IC-AI’1999, pp 177–183, Las Vegas, Nevada, USA.

    Google Scholar 

  12. Hähnle, R. Towards an efficient tableau proof procedure for multiple-valued logics. In E Börger, H Kleine Büning, M M Richter, and W Schönfeld, eds, Selected Papers from CSL’90, Heidelberg, Germany, LNCS533, pp. 248–260. Springer-Verlag, 1991.

    Google Scholar 

  13. Hähnle, R. Automated Deduction in Multiple-valued Logics. Oxford UP, 1993.

    Google Scholar 

  14. Kracht, M, On Extensions of Intermediate Logics by Strong Negation, J Philosophical Logic 27 (1998).

    Google Scholar 

  15. Lifschitz, V, Foundations of Logic Programming, in G Brewka (ed), Principles of Knowledge Representation, CSLI Publications, 1996.

    Google Scholar 

  16. Lifschitz, V, Tang, L R and Turner, H, Nested Expressions in Logic Programs, to appear in Annals of Mathematics and Artificial Intelligence.

    Google Scholar 

  17. Lukasiewicz, J, Die Logik und das Grundlagenproblem, in Les Entreties de Zürich sur les Fondaments et la Méthode des Sciences Mathématiques 6–9, 12 (1938).

    Google Scholar 

  18. Maksimova, L, Craig’s interpolation theorem and amalgamable varieties, Doklady Akademii Nauk SSSR, 237, no. 6, (1977), pp. 1281–1284.

    MathSciNet  Google Scholar 

  19. Murray, N V and Rosenthal, E. Improving tableau deductions in multiple-valued logics. In Proc 21st ISMVL, pp. 230–237, Victoria, May 1991. IEEE Press.

    Google Scholar 

  20. Murray, N V and Rosenthal, E. Adapting classical inference techniques to multiple-valued logics using signed formulas. Fundamenta Informaticae, 21(3), 1994

    Google Scholar 

  21. Nelson, D, Constructible Falsity, J Symbolic Logic 14 (1949), 16–26.

    Article  MATH  MathSciNet  Google Scholar 

  22. Niemelä, I and Simons, P, Smodels-an Implementation of the Stable Model and Well-founded Semantics, Proc LPNMR 97, Springer, 420–29.

    Google Scholar 

  23. Ojeda, M, P. de Guzmán, I, Aguilera, G and Valverde, A. Reducing signed propositional formulas. Soft Computing, vol. 2(4):157–166, 1998.

    Google Scholar 

  24. Pearce, D, A New Logical Characterisation of Stable Models and Answer Sets, in J Dix, L M Pereira, and T Przymusinski (eds), Non-monotonic Extensions of Logic Programming. Proc NMELP 96. Springer, LNAI 1216, 1997.

    Google Scholar 

  25. Pearce, D, From Here to There: Stable Negation in Logic Programming, in D Gabbay and H Wansing (eds), What is Negation?, Kluwer, 1999.

    Google Scholar 

  26. Pearce, D, P. de Guzmán, I, and Valverde, A, A Tableau System for Equilibrium Entailment, Proc TABLEAUX 2000 (To appear).

    Google Scholar 

  27. Simons, P, Extending the Stable Model Semantics with more Expressive Rules, in M Gelfond, N Leone and G Pfeifer (eds), Proc. LPNMR’99, LNAI 1730, Springer.

    Google Scholar 

  28. Smetanich, Ya, S, On Completeness of a Propositional Calculus with an additional Operation of One Variable (in Russian). Trudy Moscovskogo matrmaticheskogo obshchestva, 9 (1960), 357–372.

    Google Scholar 

  29. Valverde, A. D-Arboles de implicantes e implicados y reducciones de lógicas signadas en ATPs. PhD thesis, Universidad de Málaga, España, July 1998.

    Google Scholar 

  30. Vorob’ev, N N, A Constructive Propositional Calculus with Strong Negation (in Russian), Doklady Akademii Nauk SSR 85 (1952), 465–468.

    MathSciNet  Google Scholar 

  31. Vorob’ev, N N, The Problem of Deducibility in Constructive Propositional Calculus with Strong Negation (in Russian), Doklady Akademii Nauk SSR 85 (1952).

    Google Scholar 

  32. Wójcicki, R, Theory of Logical Calculi, Kluwer, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DFKI, Saarbrücken, Germany

    David Pearce

  2. Dept. of Applied Mathematics, University of Málaga, Spain

    Inmaculada P. de Guzmán & Agustín Valverde

Authors
  1. David Pearce
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Inmaculada P. de Guzmán
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Agustín Valverde
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Australian National University, Australia

    John Lloyd

  2. Simon Fraser University, Canada

    Veronica Dahl

  3. Universität Koblenz, Germany

    Ulrich Furbach

  4. The University of Birmingham, UK

    Manfred Kerber

  5. University of Manchester, UK

    Kung-Kiu Lau

  6. The Pennsylvania State University, USA

    Catuscia Palamidessi

  7. Universidade Nova de Lisboa, Portugal

    Luís Moniz Pereira

  8. The Hebrew University of Jerusalem, Israel

    Yehoshua Sagiv

  9. The University of Melbourne, Australia

    Peter J. Stuckey

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pearce, D., de Guzmán, I.P., Valverde, A. (2000). Computing Equilibrium Models Using Signed Formulas. In: Lloyd, J., et al. Computational Logic — CL 2000. CL 2000. Lecture Notes in Computer Science(), vol 1861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44957-4_46

Download citation

  • DOI: https://doi.org/10.1007/3-540-44957-4_46

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67797-0

  • Online ISBN: 978-3-540-44957-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation