We present a query language called MDatalog, which is an extension of Datalog for multimodal deductive databases. We define modal relational algebras and give the seminaive evaluation algorithm and the magic-set transformation for MDatalog queries. Results of this paper are proved for the multimodal logics of belief KDI4 s 5, KDI45, KD4 s 5 s , KD45(m), which are extensions of the monomodal logic KD45. We show that MDatalog has PTIME data complexity in these logics.


Modal Logic Logic Programming Predicate Symbol Kripke Model Constant Symbol 
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  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison Wesley, Reading (1995)zbMATHGoogle Scholar
  2. 2.
    Behrend, A., Manthey, R.: Update propagation in deductive databases using soft stratification. In: Benczúr, A.A., Demetrovics, J., Gottlob, G. (eds.) ADBIS 2004. LNCS, vol. 3255, pp. 22–36. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Chomicki, J.: Temporal query languages: A survey. In: Gabbay, D.M., Ohlbach, H.J. (eds.) ICTL 1994. LNCS, vol. 827, pp. 506–534. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  4. 4.
    Cumbo, C., Faber, W., Greco, G., Leone, N.: Enhancing the magic-set method for disjunctive datalog programs. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 371–385. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Debart, F., Enjalbert, P., Lescot, M.: Multimodal logic programming using equational and order-sorted logic. Theoretical Computer Science 105, 141–166 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fitting, M., Mendelsohn, R.L.: First-Order Modal Logic. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  7. 7.
    Halpern, J.Y., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artif. Intell. 54(2), 319–379 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Nguyen, L.A.: The modal query language MDatalog. Fundamenta Informaticae 46(4), 315–342 (2001)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Nguyen, L.A.: A fixpoint semantics and an SLD-resolution calculus for modal logic programs. Fundamenta Informaticae 55(1), 63–100 (2003)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Nguyen, L.A.: Multimodal logic programming and its applications to modal deductive databases (2003), Manuscript (served as a technical report), available on Internet at,
  11. 11.
    Nguyen, L.A.: The modal logic programming system MProlog. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 266–278. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Nonnengart, A.: How to use modalities and sorts in Prolog. In: MacNish, C., Moniz Pereira, L., Pearce, D.J. (eds.) JELIA 1994. LNCS, vol. 838, pp. 365–378. Springer, Heidelberg (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Linh Anh Nguyen
    • 1
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland

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