A Numerical Optimisation Based Characterisation of Spatial Reasoning

  • Carl SchultzEmail author
  • Mehul Bhatt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9718)


We present a novel numerical optimisation based characterisation of spatial reasoning in the context of constraint logic programming (CLP). The approach —formalised and implemented within CLP— is developed as an extension to CLP(QS), a declarative spatial reasoning framework providing a range of mixed quantitative-qualitative spatial representation and reasoning capabilities. We demonstrate the manner in which the numerical optimisation based extensions further enhance the declarative spatial reasoning capabilities of CLP(QS).


Numerical optimisation Declarative spatial reasoning Constraint logic programming Geometric and spatial reasoning 


  1. 1.
    Center for genomic pathology. Accessed 03 Apr 2016
  2. 2.
    Aiello, M., Pratt-Hartmann, I.E., van Benthem, J.F.A.K.: Handbook of Spatial Logics. Springer New York Inc., Secaucus (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bhatt, M., Guesgen, H., Wölfl, S., Hazarika, S.: Qualitative spatial and temporal reasoning: emerging applications, trends, and directions. Spat. Cogn. Comput. 11(1), 1–14 (2011)Google Scholar
  4. 4.
    Bhatt, M., Lee, J.H., Schultz, C.: CLP(QS): a declarative spatial reasoning framework. In: Egenhofer, M., Giudice, N., Moratz, R., Worboys, M. (eds.) COSIT 2011. LNCS, vol. 6899, pp. 210–230. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Byrd, R.H., Lu, P., Nocedal, J., Ciyou, Z.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5), 1190–1208 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cohn, A.G., Gotts, N.M.: The ‘egg-yolk’ representation of regions with indeterminate boundaries. Geogr. Objects Indeterminate Bound. 2, 171–187 (1996)Google Scholar
  7. 7.
    Duesmann, G.: Applying principles of knowledge representation and reasoning by integrating declarative spatial reasoning and computer vision: a prototype system for histopathology. Bachelor thesis, The University of Münster (2016)Google Scholar
  8. 8.
    Ge, J.-X., Chou, S.-C., Gao, X.-S.: Geometric constraint satisfaction using optimization methods. Comput. Aided Des. 31(14), 867–879 (1999)CrossRefzbMATHGoogle Scholar
  9. 9.
    Jaffar, J., Michaylov, S., Stuckey, P.J., Yap, R.H.: The CLP (R) language and system. ACM Trans. Program. Lang. Syst. (TOPLAS) 14(3), 339–395 (1992)CrossRefGoogle Scholar
  10. 10.
    Kapur, D., Mundy, J.L. (eds.): Geometric Reasoning. MIT Press, Cambridge (1988)Google Scholar
  11. 11.
    Light, R., Gossard, D.: Modification of geometric models through variational geometry. Comput. Aided Des. 14(4), 209–214 (1982)CrossRefGoogle Scholar
  12. 12.
    Ligozat, G.: Qualitative Spatial and Temporal Reasoning. Wiley-ISTE, London (2011)zbMATHGoogle Scholar
  13. 13.
    Pesant, G., Boyer, M.: Reasoning about solids using constraint logic programming. J. Autom. Reason. 22(3), 241–262 (1999)CrossRefzbMATHGoogle Scholar
  14. 14.
    Raffaetà, A., Frühwirth, T.: Spatio-temporal annotated constraint logic programming. In: Ramakrishnan, I.V. (ed.) PADL 2001. LNCS, vol. 1990, pp. 259–273. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. KR 92, 165–176 (1992)Google Scholar
  16. 16.
    Schultz, C., Bhatt, M.: Declarative spatial reasoning with boolean combinations of axis-aligned rectangular polytopes. In: ECAI 2014–21st European Conference on Artificial Intelligence, pp. 795–800 (2014)Google Scholar
  17. 17.
    Schultz, C., Bhatt, M.: Encoding relative orientation and mereotopology relations with geometric constraints in CLP(QS). In: 1st Workshop on Logics for Qualitative Modelling and Reasoning (LQMR 2015), Lodz, Poland, September 2015Google Scholar
  18. 18.
    Schultz, C., Bhatt, M.: Spatial symmetry driven pruning strategies for efficient declarative spatial reasoning. In: Fabrikant, S.I., Raubal, M., Bertolotto, M., Davies, C., Freundschuh, S., Bell, S. (eds.) COSIT 2015. LNCS, vol. 9368, pp. 331–353. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-23374-1_16 CrossRefGoogle Scholar
  19. 19.
    Wałęga, P.A., Bhatt, M., Schultz, C.: ASPMT(QS): non-monotonic spatial reasoning with answer set programming modulo theories. In: Calimeri, F., Ianni, G., Truszczynski, M. (eds.) LPNMR 2015. LNCS, vol. 9345, pp. 488–501. Springer, Heidelberg (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of MünsterMünsterGermany
  2. 2.University of BremenBremenGermany
  3. 3.The DesignSpace GroupBremenGermany

Personalised recommendations