Incremental Evaluation of Lattice-Based Aggregates in Logic Programming Using Modular TCLP

  • Joaquín AriasEmail author
  • Manuel Carro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11372)


Aggregates are used to compute single pieces of information from separate data items, such as records in a database or answers to a query to a logic program. The maximum and minimum are well-known examples of aggregates. The computation of aggregates in Prolog or variant-based tabling can loop even if the aggregate at hand can be finitely determined. When answer subsumption or mode-directed tabling is used, termination improves, but the behavior observed in existing proposals is not consistent. We present a framework to incrementally compute aggregates for elements in a lattice. We use the entailment and join relations of the lattice to define (and compute) aggregates and decide whether some atom is compatible with (entails) the aggregate. The semantics of the aggregates defined in this way is consistent with the LFP semantics of tabling with constraints. Our implementation is based on the TCLP framework available in Ciao Prolog, and improves its termination properties w.r.t. similar approaches. Defining aggregates that do not fit into the lattice structure is possible, but some properties guaranteed by the lattice may not hold. However, the flexibility provided by this possibility justifies its inclusion. We validate our design with several examples and we evaluate their performance.


  1. 1.
    Arias, J., Carro, M.: Description and evaluation of a generic design to integrate CLP and tabled execution. In: International Symposium on Principles and Practice of Declarative Programming, pp. 10–23. ACM, September 2016Google Scholar
  2. 2.
    Arias, J., Carro, M.: Description, implementation, and evaluation of a generic design for tabled CLP. Theory and Practice of Logic Programming (2018) (to appear)Google Scholar
  3. 3.
    Bratko, I.: Prolog Programming for Artificial Intelligence. Pearson Education, London (2001)zbMATHGoogle Scholar
  4. 4.
    Chico de Guzmán, P., Carro, M., Hermenegildo, M.V., Stuckey, P.: A general implementation framework for tabled CLP. In: Schrijvers, T., Thiemann, P. (eds.) FLOPS 2012. LNCS, vol. 7294, pp. 104–119. Springer, Heidelberg (2012). Scholar
  5. 5.
    Cui, B., Warren, D.S.: A system for tabled constraint logic programming. In: Lloyd, J., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Palamidessi, C., Pereira, L.M., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 478–492. Springer, Heidelberg (2000). Scholar
  6. 6.
    Guo, H.F., Gupta, G.: Simplifying dynamic programming via mode-directed tabling. Softw. Pract. Exp. 1, 75–94 (2008)CrossRefGoogle Scholar
  7. 7.
    Holzbaur, C.: Metastructures vs. attributed variables in the context of extensible unification. In: Bruynooghe, M., Wirsing, M. (eds.) PLILP 1992. LNCS, vol. 631, pp. 260–268. Springer, Heidelberg (1992). Scholar
  8. 8.
    Kemp, D.B., Stuckey, P.J.: Semantics of logic programs with aggregates. In: Saraswat, V.A., Ueda, K. (eds.) International Symposium on Logic Programming, pp. 387–401. October 1991Google Scholar
  9. 9.
    Pelov, N., Denecker, M., Bruynooghe, M.: Well-founded and stable semantics of logic programs with aggregates. Theory Pract. Log. Program. 3, 301–353 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Picard, G.: Artificial intelligence - implementing minimax with prolog.
  11. 11.
    Santos Costa, V., Rocha, R., Damas, L.: The YAP prolog system. Theory Pract. Log. Program. 1–2, 5–34 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Schrijvers, T., Demoen, B., Warren, D.S.: TCHR: a Framework for tabled CLP. Theory Pract. Log. Program. 4, 491–526 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Swift, T., Warren, D.S.: Tabling with answer subsumption: implementation, applications and performance. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 300–312. Springer, Heidelberg (2010). Scholar
  14. 14.
    Swift, T., Warren, D.S.: XSB: extending prolog with tabled logic programming. Theory Pract. Log. Program. 1–2, 157–187 (2012)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Vandenbroucke, A., Pirog, M., Desouter, B., Schrijvers, T.: Tabling with sound answer subsumption. Theory Pract. Log. Program. 16(5–6), 933–949 (2016). 32nd International Conference on Logic ProgrammingMathSciNetCrossRefGoogle Scholar
  16. 16.
    Zhou, N.F.: The language features and architecture of B-Prolog. Theory Pract. Log. Program. 1–2, 189–218 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhou, N.F., Kameya, Y., Sato, T.: Mode-directed tabling for dynamic programming, machine learning, and constraint solving. In: International Conference on Tools with Artificial Intelligence, No. 2, pp. 213–218. IEEE, October 2010Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.IMDEA Software Institute and Universidad Politécnica de MadridMadridSpain

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