Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Equivalence between Extended Datalog Programs — A Brief Survey

  • Conference paper
Datalog Reloaded (Datalog 2.0 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6702))

Included in the following conference series:

  • 1031 Accesses

Abstract

This paper gives a brief overview about the research field on equivalences in Answer-Set Programming. More precisely, we are concerned here with disjunctive logic programs under the stable-model semantics. Such programs can be understood as extended datalog queries (i.e., datalog augmented by default negation and disjunction). In particular, we shall report on characterizations and complexity results for the notions of strong and respectively uniform equivalence. Most notably, uniform equivalence becomes undecidable in the presence of default negation, while strong equivalence remains decidable for full disjunctive datalog. We also consider a restricted setting where the arity of predicates is bounded by a fixed constant.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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.

Similar content being viewed by others

References

  1. Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  2. Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and Expressive Power of Logic Programming. ACM Computing Surveys 33(3), 374–425 (2001)

    Article  Google Scholar 

  3. de Jongh, D., Hendriks, L.: Characterizations of Strongly Equivalent Logic Programs in Intermediate Logics. Theory and Practice of Logic Programming 3(3), 259–270 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Denecker, M., Vennekens, J., Bond, S., Gebser, M., Truszczynski, M.: The Second Answer Set Programming Competition. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 637–654. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Eiter, T., Faber, W., Fink, M., Woltran, S.: Complexity Results for Answer Set Programming with Bounded Predicate Arities and Implications. Annals of Mathematics and Artificial Intelligence 51(2-4), 123–165 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Eiter, T., Fink, M.: Uniform Equivalence of Logic Programs under the Stable Model Semantics. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 224–238. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Eiter, T., Fink, M., Tompits, H., Traxler, P., Woltran, S.: Replacements in Non-Ground Answer-Set Programming. In: Proc. KR 2006, pp. 340–351. AAAI Press, Menlo Park (2006)

    Google Scholar 

  8. Eiter, T., Fink, M., Tompits, H., Woltran, S.: On Eliminating Disjunctions in Stable Logic Programming. In: Proc. KR 2004, pp. 447–458. AAAI Press, Menlo Park (2004)

    Google Scholar 

  9. Eiter, T., Fink, M., Tompits, H., Woltran, S.: Simplifying Logic Programs Under Uniform and Strong Equivalence. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 87–99. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Eiter, T., Fink, M., Tompits, H., Woltran, S.: Strong and Uniform Equivalence in Answer-Set Programming: Characterizations and Complexity Results for the Non-Ground Case. In: Proc. AAAI 2005, pp. 695–700. AAAI Press, Menlo Park (2005)

    Google Scholar 

  11. Eiter, T., Fink, M., Tompits, H., Woltran, S.: Complexity Results for Checking Equivalence of Stratified Logic Programs. In: Proc. IJCAI 2007, pp. 330–335. AAAI Press, Menlo Park (2007)

    Google Scholar 

  12. Eiter, T., Fink, M., Woltran, S.: Semantical Characterizations and Complexity of Equivalences in Answer Set Programming. ACM Transactions on Computational Logic 8(3), pages 53 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Eiter, T., Gottlob, G., Gurevich, Y.: Normal Forms for Second-Order Logic over Finite Structures, and Classification of NP Optimization Problems. Annals of Pure and Applied Logic 78(1-3), 111–125 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  15. Eiter, T., Tompits, H., Woltran, S.: On Solution Correspondences in Answer Set Programming. In: Proc. IJCAI 2005, pp. 97–102. Professional Book Center (2005)

    Google Scholar 

  16. Faber, W., Pfeifer, G., Leone, N., Dell’Armi, T., Ielpa, G.: Design and Implementation of Aggregate Functions in the DLV System. Theory and Practice of Logic Programming 8(5-6), 545–580 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Feder, T., Saraiya, Y.: Decidability and Undecidability of Equivalence for Linear Datalog with Applications to Normal-Form Optimizations. In: Hull, R., Biskup, J. (eds.) ICDT 1992. LNCS, vol. 646, pp. 297–311. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  18. Fink, M.: A General Framework for Equivalences in Answer-Set Programming by Countermodels in the Logic of Here-and-There. CoRR, abs/1006.3021 (2010) (to appear); Theory and Practice of Logic Programming

    Google Scholar 

  19. Fink, M., Pichler, R., Tompits, H., Woltran, S.: Complexity of Rule Redundancy in Non-Ground Answer-Set Programming over Finite Domains. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 123–135. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. Gaifman, H., Mairson, H., Sagiv, Y., Vardi, M.: Undecidable Optimization Problems for Database Logic Programs. Journal of the ACM 40(3), 683–713 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gebser, M., Liu, L., Namasivayam, G., Neumann, A., Schaub, T., Truszczynski, M.: The First Answer Set Programming System Competition. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 3–17. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Gelfond, M.: Representing Knowledge in A-Prolog. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS (LNAI), vol. 2408, pp. 413–451. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Gelfond, M., Leone, N.: Logic Programming and Knowledge Representation - The A-Prolog Perspective. Artificial Intelligence 138(1-2), 3–38 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. Gelfond, M., Lifschitz, V.: The Stable Model Semantics for Logic Programming. In: Proc. ICLP 1988, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  25. Gelfond, M., Lifschitz, V.: Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing 9, 365–385 (1991)

    Article  MATH  Google Scholar 

  26. Halevy, A., Mumick, I., Sagiv, Y., Shmueli, O.: Static Analysis in Datalog Extensions. Journal of the ACM 48(5), 971–1012 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hillebrand, G., Kanellakis, P., Mairson, H., Vardi, M.: Tools for Datalog Boundedness. In: Proc. PODS 1991, pp. 1–12. ACM Press, New York (1991)

    Google Scholar 

  28. Inoue, K., Sakama, C.: Equivalence of Logic Programs Under Updates. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 174–186. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  29. Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV System for Knowledge Representation and Reasoning. ACM Transactions on Computational Logic 7(3), 499–562 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  30. Levy, A., Sagiv, Y.: Queries Independent of Updates. In: Proc. VLDB 1993, pp. 171–181. Morgan Kaufmann, San Francisco (1993)

    Google Scholar 

  31. Lifschitz, V.: Answer Set Programming and Plan Generation. Artificial Intelligence 138, 39–54 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. Lifschitz, V., Pearce, D., Valverde, A.: Strongly Equivalent Logic Programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  33. Lifschitz, V., Pearce, D., Valverde, A.: A Characterization of Strong Equivalence for Logic Programs with Variables. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 188–200. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  34. Lin, F.: Reducing Strong Equivalence of Logic Programs to Entailment in Classical Propositional Logic. In: Proc. KR 2002, pp. 170–176. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  35. Lin, F., Chen, Y.: Discovering Classes of Strongly Equivalent Logic Programs. Journal of Artificial Intelligence Research 28, 431–451 (2007)

    MathSciNet  MATH  Google Scholar 

  36. Liu, L., Truszczynski, M.: Properties and Applications of Programs with Monotone and Convex Constraints. Journal of Artificial Intelligence Research 27, 299–334 (2006)

    MathSciNet  MATH  Google Scholar 

  37. Maher, M.: Equivalences of Logic Programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 627–658. Morgan Kaufmann, San Francisco (1988)

    Chapter  Google Scholar 

  38. Marek, V., Truszczyński, M.: Stable Models and an Alternative Logic Programming Paradigm. In: Apt, K., Marek, V.W., Truszczyński, M., Warren, D.S. (eds.) The Logic Programming Paradigm – A 25-Year Perspective, pp. 375–398. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  39. Minker, J.: Overview of Disjunctive Logic Programming. Annals of Mathematics and Artificial Intelligence 12, 1–24 (1994)

    Article  MathSciNet  Google Scholar 

  40. Niemelä, I.: Logic Programming with Stable Model Semantics as Constraint Programming Paradigm. Annals of Mathematics and Artificial Intelligence 25(3-4), 241–273 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  41. Nogueira, M., Balduccini, M., Gelfond, M., Watson, R., Barry, M.: An A-Prolog Decision Support System for the Space Shuttle. In: Gupta, G. (ed.) PADL 1999. LNCS, vol. 1551, pp. 169–183. Springer, Heidelberg (1999)

    Google Scholar 

  42. Oetsch, J., Tompits, H.: Program Correspondence under the Answer-Set Semantics: The Non-ground Case. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 591–605. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  43. Oikarinen, E., Janhunen, T.: Modular Equivalence for Normal Logic Programs. In: Proc. ECAI 2006, pp. 412–416. IOS Press, Amsterdam (2006)

    Google Scholar 

  44. Pearce, D., Tompits, H., Woltran, S.: Characterising Equilibrium Logic and Nested Logic Programs: Reductions and Complexity. Theory and Practice of Logic Programming 9(5), 565–616 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  45. Pearce, D., Valverde, A.: Uniform Equivalence for Equilibrium Logic and Logic Programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 194–206. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  46. Sagiv, Y.: Optimising DATALOG Programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 659–698. Morgan Kaufmann, San Francisco (1988)

    Chapter  Google Scholar 

  47. Schaub, T.: Making Your Hands Dirty Inspires Your Brain! Or How to Switch ASP into Production Mode. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS (LNAI), vol. 5753, pp. 631–633. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  48. Shmueli, O.: Decidability and Expressiveness Aspects of Logic Queries. In: Proc. PODS 1987, pp. 237–249. ACM Press, New York (1987)

    Google Scholar 

  49. Truszczynski, M., Woltran, S.: Relativized Hyperequivalence of Logic Programs for Modular Programming. Theory and Practice of Logic Programming 9(6), 781–819 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  50. Turner, H.: Strong Equivalence Made Easy: Nested Expressions and Weight Constraints. Theory and Practice of Logic Programming 3(4-5), 602–622 (2003)

    MathSciNet  MATH  Google Scholar 

  51. Vardi, M.: The Complexity of Relational Query Languages (Extended Abstract). In: Proc. STOC 1982, pp. 137–146. ACM, New York (1982)

    Google Scholar 

  52. Vardi, M.: On the Complexity of Bounded-Variable Queries. In: Proc. PODS 1995, pp. 266–276. ACM Press, New York (1995)

    Google Scholar 

  53. Woltran, S.: Characterizations for Relativized Notions of Equivalence in Answer Set Programming. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 161–173. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  54. Woltran, S.: A common view on Strong, Uniform, and other Notions of Equivalence in Answer-Set Programming. Theory and Practice of Logic Programming 8(2), 217–234 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  55. Wong, K.-S.: Sound and Complete Inference Rules for SE-Consequence. Journal of Artificial Intelligence Research 31, 205–216 (2008)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Information Systems, Technische Universität Wien, 184/2 Favoritenstrasse 9-11, 1040, Vienna, Austria

    Stefan Woltran

Authors
  1. Stefan Woltran
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Oege de Moor

  2. Department of Computer Science, University of Oxford, UK

    Georg Gottlob , Tim Furche  & Andrew Sellers ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Woltran, S. (2011). Equivalence between Extended Datalog Programs — A Brief Survey. In: de Moor, O., Gottlob, G., Furche, T., Sellers, A. (eds) Datalog Reloaded. Datalog 2.0 2010. Lecture Notes in Computer Science, vol 6702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24206-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24206-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24205-2

  • Online ISBN: 978-3-642-24206-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation