Skip to main content
SpringerLink
Log in

Modular Paracoherent Answer Sets

  • Conference paper
Logics in Artificial Intelligence (JELIA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8761))

Included in the following conference series:

Abstract

The answer set semantics may assign a logic program no model due to classic contradiction or cyclic negation. The latter can be remedied by resorting to a paracoherent semantics given by semi-equilibrium (SEQ) models, which are 3-valued interpretations that generalize the logical reconstruction of answer sets given by equilibrium models. While SEQ-models have interesting properties, they miss modularity in the rules, such that a natural modular (bottom up) evaluation of programs is hindered. We thus refine SEQ-models using splitting sets, the major tool for modularity in modeling and evaluating answer set programs. We consider canonical models that are independent of any particular splitting sequence from a class of splitting sequences, and present two such classes whose members are efficiently recognizable. Splitting SEQ-models does not make reasoning harder, except for deciding model existence in presence of constraints (without constraints, split SEQ-models always exist).

This work was partially supported by Regione Calabria under the EU Social Fund and project PIA KnowRex POR FESR 2007- 2013, and by the Italian Ministry of University and Research under PON project “Ba2Know (Business Analytics to Know) S.I.-LAB” n. PON03PE_0001.

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. Alcântara, J., Damásio, C.V., Pereira, L.M.: A declarative characterization of disjunctive paraconsistent answer sets. In: Proc. ECAI 2004, pp. 951–952. IOS Press (2004)

    Google Scholar 

  2. Apt, K., Blair, H., Walker, A.: Towards a theory of declarative knowledge. In: Minker (ed.) [16], pp. 89–148

    Google Scholar 

  3. Balduccini, M., Gelfond, M.: Logic programs with consistency-restoring rules. In: McCarthy, J., Williams, M.A. (eds.) Int’l Symp. Logical Formalization of Commonsense Reasoning. AAAI 2003 Spring Symp. Series, pp. 9–18 (2003)

    Google Scholar 

  4. Ben-Eliyahu, R., Dechter, R.: Propositional semantics for disjunctive logic programs. Ann. Math. & Artif. Intell. 12, 53–87 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. Blair, H.A., Subrahmanian, V.S.: Paraconsistent logic programming. Theor. Comput. Sci. 68(2), 135–154 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dao-Tran, M., Eiter, T., Fink, M., Krennwallner, T.: Modular nonmonotonic logic programming revisited. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 145–159. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Eiter, T., Gottlob, G.: On the computational cost of disjunctive logic programming: Propositional case. Ann. Math. & Artif. Intell. 15(3/4), 289–323 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Eiter, T., Fink, M., Moura, J.: Paracoherent answer set programming. In: Lin, F., Sattler, U., Truszcyński, M. (eds.) Proc. KR 2010, pp. 486–496. AAAI Press, Toronto (2010)

    Google Scholar 

  9. Eiter, T., Leone, N., Saccà, D.: On the partial semantics for disjunctive deductive databases. Ann. Math. & Artif. Intell. 19(1/2), 59–96 (1997)

    Article  MATH  Google Scholar 

  10. Faber, W., Greco, G., Leone, N.: Magic sets and their application to data integration. J. Comput. Syst. Sci. 73(4), 584–609 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  12. Heyting, A.: Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften 16(1), 42–56 (1930)

    MathSciNet  Google Scholar 

  13. Huang, S., Li, Q., Hitzler, P.: Reasoning with inconsistencies in hybrid MKNF knowledge bases. Logic Journal of the IGPL 21(2), 263–290 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Janhunen, T., Oikarinen, E., Tompits, H., Woltran, S.: Modularity aspects of disjunctive stable models. J. Artif. Intell. Res. (JAIR) 35, 813–857 (2009)

    Google Scholar 

  15. Lifschitz, V., Turner, H.: Splitting a logic program. In: Proc. ICLP 1994, pp. 23–38. MIT-Press (1994)

    Google Scholar 

  16. Minker, J. (ed.): Foundations of Deductive Databases and Logic Programming. Morgan Kaufman, Washington, DC (1988)

    Google Scholar 

  17. Odintsov, S., Pearce, D.J.: Routley semantics for answer sets. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 343–355. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Osorio, M., Ramírez, J.R.A., Carballido, J.L.: Logical weak completions of paraconsistent logics. J. Log. Comput. 18(6), 913–940 (2008)

    Article  MATH  Google Scholar 

  19. Pearce, D.: Equilibrium logic. Ann. Math. & Artif. Intell. 47(1-2), 3–41 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pearce, D.J., Valverde, A.: Quantified equilibrium logic and foundations for answer set programs. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 546–560. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  21. Pereira, L.M., Alferes, J.J., Aparício, J.N.: Contradiction removal semantics with explicit negation. In: Masuch, M., Pólos, L. (eds.) Logic at Work 1992. LNCS, vol. 808, pp. 91–105. Springer (1992)

    Google Scholar 

  22. Pereira, L.M., Pinto, A.M.: Revised stable models - a semantics for logic programs. In: Bento, C., Cardoso, A., Dias, G. (eds.) EPIA 2005. LNCS (LNAI), vol. 3808, pp. 29–42. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Pereira, L.M., Pinto, A.M.: Approved models for normal logic programs. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 454–468. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  24. Pereira, L.M., Pinto, A.M.: Layered models top-down querying of normal logic programs. In: Gill, A., Swift, T. (eds.) PADL 2009. LNCS, vol. 5418, pp. 254–268. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  26. Przymusinski, T.C.: On the declarative semantics of deductive databases and logic programs. In: Minker (ed.) [16], pp. 193–216

    Google Scholar 

  27. Saccà, D., Zaniolo, C.: Partial models and three-valued stable models in logic programs with negation. In: Subrahmanian, V., et al. (eds.) Proc. LPNMR 1991, pp. 87–101. MIT Press (1991)

    Google Scholar 

  28. Sakama, C., Inoue, K.: Paraconsistent stable semantics for extended disjunctive programs. J. Log. Comput. 5(3), 265–285 (1995)

    Google Scholar 

  29. Seipel, D.: Partial evidential stable models for disjunctive deductive databases. In: Dix, J., Moniz Pereira, L., Przymusinski, T.C. (eds.) LPKR 1997. LNCS (LNAI), vol. 1471, pp. 66–84. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  30. Tarjan, R.E.: Depth-first search and linear graph algorithms. SIAM J. Comput. 1(2), 146–160 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  31. van Gelder, A., Ross, K., Schlipf, J.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–650 (1991)

    MATH  Google Scholar 

  32. You, J.H., Yuan, L.: A three-valued semantics for deductive databases and logic programs. J. Comput. Syst. Sci. 49, 334–361 (1994)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Calabria, Via P. Bucci, Cubo 30b, 87036, Rende, CS, Italy

    Giovanni Amendola & Nicola Leone

  2. Institute of Information Systems, Vienna University of Technology, Favoritenstraße 9-11, A-1040, Vienna, Austria

    Thomas Eiter

Authors
  1. Giovanni Amendola
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Eiter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicola Leone
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Madeira, Funchal, Madeira, Portugal

    Eduardo Fermé

  2. CENTRIA, Universidade Nova de Lisboa, Caparica, Portugal

    João Leite

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Amendola, G., Eiter, T., Leone, N. (2014). Modular Paracoherent Answer Sets. In: Fermé, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11558-0_32

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11557-3

  • Online ISBN: 978-3-319-11558-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation