Advertisement

Polyadic Soft Constraints

  • Filippo Bonchi
  • Laura Bussi
  • Fabio GadducciEmail author
  • Francesco Santini
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11760)

Abstract

We propose a formalism for manipulating soft constraints based on polyadic algebras. The choice of such algebras in place of classical cylindric ones simplifies the structure of the partial order of preference values by removing diagonals, a family of constants used for modelling parameter passing and variable substitution, whose presence require completeness. Removing diagonals also allows for an easy representation of preference/cost functions in terms of polynomials, thus streamlining their manipulation on languages based on (stores of) constraints. Besides presenting the main features of the new formalism, the paper investigates how the operators of polyadic algebras interact with the residuated monoid structure that is used for representing the set of preference values.

Keywords

Soft constraints Polyadic algebras Residuated monoids 

References

  1. 1.
    Aristizábal, A., Bonchi, F., Palamidessi, C., Pino, L., Valencia, F.: Deriving labels and bisimilarity for concurrent constraint programming. In: Hofmann, M. (ed.) FoSSaCS 2011. LNCS, vol. 6604, pp. 138–152. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-19805-2_10CrossRefzbMATHGoogle Scholar
  2. 2.
    Bistarelli, S., Montanari, U., Rossi, F.: Semiring-based constraint satisfaction and optimization. J. ACM 44(2), 201–236 (1997)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bistarelli, S., Gadducci, F.: Enhancing constraints manipulation in semiring-based formalisms. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) ECAI 2006. FAIA, vol. 141, pp. 63–67. IOS Press (2006)Google Scholar
  4. 4.
    Bistarelli, S., Montanari, U., Rossi, F.: Soft concurrent constraint programming. ACM Trans. Comput. Logic 7(3), 563–589 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bistarelli, S., Pini, M.S., Rossi, F., Venable, K.B.: From soft constraints to bipolar preferences: modelling framework and solving issues. Exp. Theor. Artif. Intell. 22(2), 135–158 (2010)CrossRefGoogle Scholar
  6. 6.
    de Boer, F.S., Palamidessi, C.: A fully abstract model for concurrent constraint programming. In: Abramsky, S., Maibaum, T.S.E. (eds.) CAAP 1991. LNCS, vol. 493, pp. 296–319. Springer, Heidelberg (1991).  https://doi.org/10.1007/3-540-53982-4_17CrossRefGoogle Scholar
  7. 7.
    Chiarugi, D., Falaschi, M., Olarte, C., Palamidessi, C.: A declarative view of signaling pathways. In: Bodei, C., Ferrari, G.-L., Priami, C. (eds.) Programming Languages with Applications to Biology and Security. LNCS, vol. 9465, pp. 183–201. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-25527-9_13CrossRefGoogle Scholar
  8. 8.
    De Boer, F.S., Gabbrielli, M., Marchiori, E., Palamidessi, C.: Proving concurrent constraint programs correct. ACM Trans. Program. Lang. Syst. 19(5), 685–725 (1997)CrossRefGoogle Scholar
  9. 9.
    Fages, F., Ruet, P., Soliman, S.: Linear concurrent constraint programming: operational and phase semantics. Inf. Comput. 165(1), 14–41 (2001)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gadducci, F., Santini, F.: Residuation for bipolar preferences in soft constraints. Inf. Process. Lett. 118, 69–74 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gadducci, F., Santini, F., Pino, L.F., Valencia, F.D.: Observational and behavioural equivalences for soft concurrent constraint programming. Logical Algebraic Methods Program. 92, 45–63 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Golan, J.: Semirings and Affine Equations over Them. Kluwer (2003)Google Scholar
  13. 13.
    Knight, S., Palamidessi, C., Panangaden, P., Valencia, F.D.: Spatial and epistemic modalities in constraint-based process calculi. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 317–332. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32940-1_23CrossRefGoogle Scholar
  14. 14.
    Kumar, V.: Algorithms for constraint-satisfaction problems: a survey. AI Mag. 13(1), 32–44 (1992)MathSciNetGoogle Scholar
  15. 15.
    López, H.A., Palamidessi, C., Pérez, J.A., Rueda, C., Valencia, F.D.: A declarative framework for security: secure concurrent constraint programming. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 449–450. Springer, Heidelberg (2006).  https://doi.org/10.1007/11799573_43CrossRefzbMATHGoogle Scholar
  16. 16.
    Nielsen, M., Palamidessi, C., Valencia, F.D.: Temporal concurrent constraint programming: denotation, logic and applications. Nordic J. Comput. 9(1), 145–188 (2002)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Palamidessi, C., Valencia, F.D.: A temporal concurrent constraint programming calculus. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 302–316. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-45578-7_21CrossRefzbMATHGoogle Scholar
  18. 18.
    Sági, G.: Polyadic algebras. In: Andréka, H., Ferenczi, M., Németi, I. (eds.) Cylindric-like Algebras and Algebraic Logic. BSMS, vol. 22, pp. 367–389. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-35025-2_18CrossRefGoogle Scholar
  19. 19.
    Saraswat, V.A., Rinard, M.C., Panangaden, P.: Semantic foundations of concurrent constraint programming. In: Wise, D.S. (ed.) POPL 1991, pp. 333–352. ACM Press (1991)Google Scholar
  20. 20.
    Scott, A.D., Sorkin, G.B.: Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function. ACM Trans. Algorithms 5(4), 45:1–45:27 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Filippo Bonchi
    • 1
  • Laura Bussi
    • 1
  • Fabio Gadducci
    • 1
    Email author
  • Francesco Santini
    • 2
  1. 1.Dipartimento di InformaticaUniversity of PisaPisaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversity of PerugiaPerugiaItaly

Personalised recommendations