, Volume 19, Issue 2, pp 163–173 | Cite as

Qualitative modelling via constraint programming

  • Thomas W. Kelsey
  • Lars Kotthoff
  • Christopher A. Jefferson
  • Stephen A. Linton
  • Ian Miguel
  • Peter Nightingale
  • Ian P. Gent


Qualitative modelling is a technique integrating the fields of theoretical computer science, artificial intelligence and the physical and biological sciences. The aim is to be able to model the behaviour of systems without estimating parameter values and fixing the exact quantitative dynamics. Traditional applications are the study of the dynamics of physical and biological systems at a higher level of abstraction than that obtained by estimation of numerical parameter values for a fixed quantitative model. Qualitative modelling has been studied and implemented to varying degrees of sophistication in Petri nets, process calculi and constraint programming. In this paper we reflect on the strengths and weaknesses of existing frameworks, we demonstrate how recent advances in constraint programming can be leveraged to produce high quality qualitative models, and we describe the advances in theory and technology that would be needed to make constraint programming the best option for scientific investigation in the broadest sense.


Constraint programming Qualitative models 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aggoun, A., Chan, D., Dufresne, P., Falvey, E., Grant, H., Harvey, W., Herold, A., Macartney, G., Meier, M., Miller, D., Mudambi, S., Novello, S., Perez, B., van Rossum, E., Schimpf, J., Shen, K., Tsahageas, P.A., de Villeneuve, D.H. (2006). Eclipse user manual release 5.10,
  2. 2.
    Balasubramaniam, D., de Silva, L., Jefferson, C., Kotthoff, L., Miguel, I., Nightingale, P. (2011). Dominion: an architecture-driven approach to generating efficient constraint solvers. In 9th Working IEEE/IFIP conference on software architecture (WICSA) (pp. 228–231).Google Scholar
  3. 3.
    Balasubramaniam, D., Jefferson, C., Kotthoff, L., Miguel, I., Nightingale, P. (2012). An automated approach to generating efficient constraint solvers. In 34th international conference on software engineering.Google Scholar
  4. 4.
    Beldiceanu, N., & Simonis, H. A model seeker: extracting global constraint models from positive examples. In M. Milano (Ed.), Principles and practice of constraint programming - 18th international conference, CP 2012, Quebec City, QC, Canada, October 8–12, 2012. Proceedings, lecture notes in computer science (vol. 7514, pp. 141–157). Springer.Google Scholar
  5. 5.
    Bockmayr, A., & Courtois, A. (2002). Using hybrid concurrent constraint programming to model dynamic biological systems. In 18th international conference on logic programming (pp. 85–99). Springer.Google Scholar
  6. 6.
    Bristol-Gould, S.K., Kreeger, P.K., Selkirk, C.G., Kilen, S.M., Mayo, K.E., Shea, L.D., Woodruff, T.K. (2006). Fate of the initial follicle pool: empirical and mathematical evidence supporting its sufficiency for adult fertility. Developmental biology, 298(1), 149–54.CrossRefGoogle Scholar
  7. 7.
    Calder, M., & Hillston, J. (2009). Process algebra modelling styles for biomolecular processes. In C. Priami, R.J. Back, I. Petre (Eds), Transactions on computational systems biology XI (pp. 1–25). Berlin, Heidelberg: Springer-Verlag.Google Scholar
  8. 8.
    Calzone, L., Chabrier-Rivier, N., Fages, F., Soliman, S. (2006). Machine learning biochemical networks from temporal logic properties. The Computer System Biology, 68–94.Google Scholar
  9. 9.
    Calzone, L., Fages, F., Soliman, S. (2006). BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge. Bioinformatics (Oxford, England), 22(14), 1805–7.CrossRefGoogle Scholar
  10. 10.
    Cimatti, A., Micheli, A., Roveri, M. Solving temporal problems using smt: Strong controllability. In M. Milano (Ed.), Principles and practice of constraint programming - 18th international conference, CP 2012, Quebec City, QC, Canada, October 8–12, 2012. Proceedings, lecture notes in computer science (vol. 7514, pp. 248–264).Google Scholar
  11. 11.
    Ciocchetta, F., & Hillston, J. (2009). Bio-pepa: a framework for the modelling and analysis of biological systems. Theoretical Computer Science, 410(33-34), 3065–3084.CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Clancy, D. (1998). Qualitative simulation as a temporally-extended constraint satisfaction problem. Proceedings AAAI, 98.Google Scholar
  13. 13.
    Degasperi, A., & Calder, M. (2009). On the formalisation of gradient diffusion models of biological systems. In Proceedings 8th workshop on process algebra and stochastically timed activities (pp. 139–144).Google Scholar
  14. 14.
    Distler, A., Kelsey, T., Kotthoff, L., Jefferson, C. (2012). The semigroups of order 10. In CP. lecture notes in computer science (vol. 7514, pp. 883–899). Springer.Google Scholar
  15. 15.
    Distler, A., & Kelsey, T. (2009). The monoids of orders eight, nine & ten. Annals of Mathematics and Artificial Intelligence, 56(1), 3–21.CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Distler, A., & Kelsey, T. (2013). The semigroups of order 9 and their automorphism groups. Semigroup Forum, 1–20.Google Scholar
  17. 17.
    Escrig, M.T., Cabedo, L.M., Pacheco, J., Toledo, F. (2002). Several models on qualitative motion as instances of the CSP. Revista Iberoamericana de Inteligencia Artificial, 6(17), 55–71.Google Scholar
  18. 18.
    Faddy, M.J., & Gosden, R.G. (1995). A mathematical model of follicle dynamics in the human ovary. Human reproduction (Oxford, England), 10(4), 770–5.Google Scholar
  19. 19.
    Fleming, R., Kelsey, T.W., Anderson, R.A., Wallace, W.H., Nelson, S.M. (2012). Interpreting human follicular recruitment and antimullerian hormone concentrations throughout life. Fertility and Sterility, 98(5), 1097–1102.CrossRefGoogle Scholar
  20. 20.
    Frisch, A.M., Harvey, W., Jefferson, C., Martínez-Hernández, B., Miguel, I. (2008). Essence: a constraint language for specifying combinatorial problems. Constraints, 13(3), 268–306.CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Gent, I.P., Jefferson, C., Miguel, I. (2006). Minion: a fast scalable constraint solver. In G. Brewka, S. Coradeschi, A. Perini, P. Traverso (Eds.), The European conference on artificial intelligence 2006 (ECAI 06) (pp. 98-102). IOS Press.Google Scholar
  22. 22.
    Gent, I.P., Jefferson, C.A., Miguel, I. (2006). MINION: a fast scalable constraint solver. In Proceedings of the 17th european conference on artificial intelligence (pp. 98–102).Google Scholar
  23. 23.
    Haefner, J. (2005). Modeling biological systems. New York: Springer-Verlag.zbMATHGoogle Scholar
  24. 24.
    Hentenryck, P.V., Hentenryck, P.V., Michel, L., Michel, L. (1997). Newton: constraint programming over nonlinear real constraints. In Science of computer programming (pp. 1–2). Numerica: MIT Press.Google Scholar
  25. 25.
    Hoda, S., van Hoeve, W.J., Hooker, J.N. (2010). A systematic approach to MDD-based constraint programming. In D. Cohen (Ed.), CP. Lecture notes in computer science (vol. 6308, pp. 266–280). Springer.Google Scholar
  26. 26.
    Hutter, F., Hoos, H.H., Leyton-Brown, K., Stützle, T. (2009). Paramils: an automatic algorithm configuration framework. Journal of Artificial Intelligence Research, 36(1), 267–306.zbMATHGoogle Scholar
  27. 27.
    Jefferson, C., Moore, N., Nightingale, P., Petrie, K.E. (2010). Implementing logical connectives in constraint programming. Artificial Intelligence, 174, 1407–1429.CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Kelsey, T.W., Anderson, R.A., Wright, P., Nelson, S.M., Wallace, W.H.B. (2011). Data-driven assessment of the human ovarian reserve. Molecular human reproduction, 18(2), 79–87.CrossRefGoogle Scholar
  29. 29.
    Kelsey, T., & Linton, S. (2012). Qualitative models of cell dynamics as constraint satisfaction problems. In R. Backhoven, S. Will (Eds.), Proceedings of the workshop on constraint based methods for bioinformatics (WCB12) (pp. 16–22).Google Scholar
  30. 30.
    Ko, K.I. (1984). On the computational complexity of ordinary differential equations. Information and Control, 58(1-3), 157–194.CrossRefGoogle Scholar
  31. 31.
    Kuipers, B. (1993). Reasoning with qualitative models. Artificial Intelligence, 59, 125–132.CrossRefGoogle Scholar
  32. 32.
    Laburthe, F. Choco: a constraint programming kernel for solving combinatorial optimization problems,
  33. 33.
    Menzies, T., & Compton, P. (1997). Applications of abduction: hypothesis testing of neuroendocrinological qualitative compartmental models. Artificial Intelligence in Medicine, 10(2), 145–75.CrossRefGoogle Scholar
  34. 34.
    Menzies, T., Compton, P., Feldman, B., Toth, T. (1992). Qualitative compartmental modelling. AAAI Technical Report SS-92-02.Google Scholar
  35. 35.
    Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G. (2007). Minizinc: towards a standard cp modelling language. In Proceedings of 13th international conference on principles and practice of constraint programming (pp. 529–543).Google Scholar
  36. 36.
    Radke-Sharpe, N., & White, K. (1998). The role of qualitative knowledge in the formulation of compartmental models. IEEE Transactions on Systems, Man and Cybernetics Part C (Applications and Reviews), 28(2), 272–275.CrossRefGoogle Scholar
  37. 37.
    Rendl, A., Miguel, I., Gent, I.P., Jefferson, C. (2009). Automatically enhancing constraint model instances during tailoring. In Proceedings of 8th symposium on abstraction, reformulation, and approximation (SARA).Google Scholar
  38. 38.
    Rice, J.R. (1976). The algorithm selection problem. Advances in Computers, 15, 65–118.CrossRefGoogle Scholar
  39. 39.
    Rizk, A., Batt, G., Fages, F., Soliman, S. (2011). Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures. Theoretical Computer Science, 412(26), 2827–2839.CrossRefzbMATHMathSciNetGoogle Scholar
  40. 40.
    Robertson, D., Bundy, A., Meutzelfeldt, R., Haggith, M., Uschold, M. (1991). Eco-logic: logic-based approaches to ecological modelling. MIT Press.Google Scholar
  41. 41.
    Tsoukias, N.M. (2008). Nitric oxide bioavailability in the microcirculation: insights from mathematical models. Microcirculation (New York, N.Y. : 1994), 15(8), 813–34.CrossRefGoogle Scholar
  42. 42.
    Wallace, W.H.B., & Kelsey, T.W. (2010). Human ovarian reserve from conception to the menopause. PloS one, 5(1), e8772.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Thomas W. Kelsey
    • 1
  • Lars Kotthoff
    • 2
  • Christopher A. Jefferson
    • 1
  • Stephen A. Linton
    • 1
  • Ian Miguel
    • 1
  • Peter Nightingale
    • 1
  • Ian P. Gent
    • 1
  1. 1.School of Computer ScienceUniversity of St AndrewsSt AndrewsUK
  2. 2.INSIGHT Centre for Data AnalyticsUniversity College CorkCorkIreland

Personalised recommendations