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European Workshop on Logics in Artificial Intelligence

JELIA 2004: Logics in Artificial Intelligence pp 134–146Cite as

Capturing Parallel Circumscription with Disjunctive Logic Programs

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3229))

Abstract

The stable model semantics of disjunctive logic programs is based on classical models which are minimal with respect to subset inclusion. As a consequence, every atom appearing in a disjunctive program is false by default. This is sometimes undesirable from the knowledge representation point of view and a more refined control of minimization is called for. Such features are already present in Lifschitz’s parallel circumscription where certain atoms are allowed to vary or to have fixed values while all other atoms are minimized. In this paper, it is formally shown that the expressive power of minimal models is properly increased in the presence of varying atoms. In spite of this, we show how parallel circumscription can be embedded into disjunctive logic programming in a relatively systematic fashion using a linear and faithful, but non-modular translation. This enables the conscious use of varying atoms in disjunctive logic programs — leading to more elegant and concise problem representations in various domains.

The research reported in this paper has been partially funded by the Academy of Finland (project #53695) and the European Commission (contract IST-FET-2001-37004).

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References

  1. Baumgartner, P., Fröhlich, P., Furbach, U., Nejdl, W.: Semantically guided theorem proving for diagnosis applications. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence, Nagoya, pp. 460–465. Morgan Kaufmann, San Francisco (1997)

    Google Scholar 

  2. Cadoli, M., Eiter, T., Gottlob, G.: An efficient method for eliminating varying predicates from a circumscription. Artificial Intelligence 54(2), 397–410 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. de Kleer, J., Konolige, K.: Eliminating the fixed predicates from a circumscription. Artificial Intelligence 39(3), 391–398 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  4. Eiter, T., Faber, W., Leone, N., Pfeifer, G.: The diagnosis frontend of the DLV system. AI Communications 12(1-2), 99–111 (1999)

    MathSciNet  Google Scholar 

  5. Eiter, T., Gottlob, G.: On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence 15, 289–323 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Eiter, T., Gottlob, G., Veith, H.: Modular logic programming and generalized quantifiers. In: Dix, J., Furbach, U., Nerode, A. (eds.) LPNMR 1997. LNCS (LNAI), vol. 1265, pp. 289–308. Springer, Heidelberg (1997)

    Google Scholar 

  7. Gelfond, M., Lifschitz, V.: Compiling circumscriptive theories into logic programs. In: Proceedings of the 7th National Conference on Artificial Intelligence, St. Paul, MN, August 1988, pp. 449–455. AAAI Press, Menlo Park (1988)

    Google Scholar 

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

    Article  Google Scholar 

  9. Inoue, K., Sakama, C.: Negation as failure in the head. Journal of Logic Programming 35(1), 39–78 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Janhunen, T.: On the intertranslatability of non-monotonic logics. Annals of Mathematics and Artificial Intelligence 27(1-4), 79–128 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Janhunen, T.: On the effect of default negation on the expressiveness of disjunctive rules. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 93–106. Springer, Heidelberg (2001)

    Google Scholar 

  12. Janhunen, T.: Translatability and intranslatability results for certain classes of logic programs, Espoo, Finland. Series A: Research report 82, Helsinki University of Technology, Laboratory for Theoretical Computer Science (November 2003)

    Google Scholar 

  13. Janhunen, T., Niemelä, I., Seipel, D., Simons, P., You, J.-H.: Unfolding partiality and disjunctions in stable model semantics. ACM Transactions on Computational Logic (2004), Accepted for publication, see http://www.acm.org/tocl/accepted.html

  14. Lee, J., Lin, F.: Loop formulas for circumscription. In: Proceedings of the 19th National Conference on Artificial Intelligence, San Jose, California, July 2004, pp. 281–286. AAAI, Menlo Park (2004)

    Google Scholar 

  15. Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Scarcello, F.: The DLV system for knowledge representation and reasoning. CoRR: cs.AI/0211004 v2 (August 2003)

    Google Scholar 

  16. Lifschitz, V.: Computing circumscription. In: Proceedings of the 9th International Joint Conference on Artificial Intelligence, Los Angeles, California, USA, August 1985, pp. 121–127. Morgan Kaufmann, San Francisco (1985)

    Google Scholar 

  17. Lifschitz, V., Turner, H.: Splitting a logic program. In: Proceedings of the 11th International Conference on Logic Programming, pp. 23–37. MIT Press, Cambridge (1994)

    Google Scholar 

  18. McCarthy, J.: Circumscription—a form of non-monotonic reasoning. Artificial Intelligence 13, 27–39 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  19. Niemelä, I.: A tableau calculus for minimal model reasoning. In: Miglioli, P., Moscato, U., Ornaghi, M., Mundici, D. (eds.) TABLEAUX 1996. LNCS, vol. 1071, pp. 278–294. Springer, Heidelberg (1996)

    Google Scholar 

  20. Przymusinski, T.C.: Stable semantics for disjunctive programs. New Generation Computing 9, 401–424 (1991)

    Article  Google Scholar 

  21. Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32, 57–95 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  22. Sakama, C., Inoue, K.: Embedding circumscriptive theories in general disjunctive programs. In: Marek, V.W., Truszczyński, M., Nerode, A. (eds.) LPNMR 1995. LNCS, vol. 928, pp. 344–357. Springer, Heidelberg (1995)

    Google Scholar 

  23. Simons, P.: Extending the stable model semantics with more expressive rules. In: Gelfond, M., Leone, N., Pfeifer, G. (eds.) LPNMR 1999. LNCS (LNAI), vol. 1730, pp. 305–316. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratory for Theoretical Computer Science, Helsinki University of Technology, P.O. Box 5400, FIN-02015 HUT, Finland

    Tomi Janhunen & Emilia Oikarinen

Authors
  1. Tomi Janhunen
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  2. Emilia Oikarinen
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Editor information

Editors and Affiliations

  1. CENTRIA, Universidade Nova de Lisboa, Portugal

    Jóse Júlio Alferes

  2. Departamento de Informática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    João Leite

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Janhunen, T., Oikarinen, E. (2004). Capturing Parallel Circumscription with Disjunctive Logic Programs. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_14

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  • DOI: https://doi.org/10.1007/978-3-540-30227-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23242-1

  • Online ISBN: 978-3-540-30227-8

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