Abstract
In this paper we present a novel framework and full implementation of probabilistic spatial reasoning within a Logic Programming context. The crux of our approach is extending Probabilistic Logic Programming (based on distribution semantics) to support reasoning over spatial variables via Constraint Logic Programming. Spatial reasoning is formulated as a numerical optimisation problem, and we implement our approach within ProbLog 1. We demonstrate a range of powerful features beyond what is currently provided by existing probabilistic and spatial reasoning tools.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Importantly, observe that the probabilities do not state that the dc relation holds with probability 0.8; this cannot be the case as dc and ec are mutually exclusive, and yet the probabilities 0.8 and 0.56 sum to more than 1. Such an inference would require information about the spatial distribution of the objects which has not been given in the problem description.
- 2.
Specifically, we have used the original ProbLog 1 implemented in Yap Prolog v6.3.4 with the default ProbLog algorithm flags and settings when consulted.
- 3.
We employ the egg-yolk method of modelling regions with indeterminante boundaries [6] to characterise a class of regions (including polygons) that satisfies topological and relative orientation relations [19]. Each egg-yolk region is an equivalence class for all regions that are contained within the upper approximation (the egg white), and completely contain the lower approximations (the egg yolk).
- 4.
To clarify, there are an infinite number of 2D points defined by two real coordinates, and so the spatial domain of 2D points is infinite in size. Similarly the domains of lines, circles, egg-yolk regions, and polygons are infinite.
- 5.
- 6.
References
Aiello, M., Pratt-Hartmann, I.E., van Johan Benthem, F.A.K.: Handbook of Spatial Logics. Springer, Secaucus (2007)
Arnon, D.S., Collins, G.E., McCallum, S.: Cylindrical algebraic decomposition I: the basic algorithm. SIAM J. Comput. 13(4), 865–877 (1984)
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)
Bouhineau, D.: Solving geometrical constraint systems using CLP based on linear constraint solver. In: Calmet, J., Campbell, J.A., Pfalzgraf, J. (eds.) AISMC-3. LNCS, vol. 1138, pp. 274–288. Springer, Heidelberg (1996)
Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5), 1190–1208 (1995)
Cohn, A.G., Gotts, N.M.: The ‘egg-yolk’ representation of regions with indeterminate boundaries. Geogr. Objects Indeterminate Boundaries 2, 171–187 (1996)
de Moura, L., Bjørner, N.S.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
De Raedt, L., Kimmig, A., Toivonen, H.: Problog: a probabilistic prolog and its application in link discovery. In: IJCAI, vol. 7, pp. 2462–2467 (2007)
Gantner, Z., Westphal, M., Wölfl, S.: GQR-A fast reasoner for binary qualitative constraint calculi. In: Proceedings of AAAI, vol. 8 (2008)
Ge, J.-X., Chou, S.-C., Gao, X.-S.: Geometric constraint satisfaction using optimization methods. Comput. Aided Des. 31(14), 867–879 (1999)
Girlea, C., Amir, E.: Probabilistic region connection calculus. In: Workshop on Spatio-temporal Dynamics, Co-located at the European Conference on Artifcial Intelligence (ECAI 2012), pp. 62–67 (2012)
Gutmann, B.: On continuous distributions and parameter estimation in probabilistic logic programs. Ph.D. dissertation, Ph. D thesis, KULeuven (2011)
Jaffar, J., Michaylov, S., Stuckey, P.J., Yap, R.H.C.: The CLP (R) language and system. ACM Trans. Program. Lang. Syst. (TOPLAS) 14(3), 339–395 (1992)
Kapur, D., Mundy, J.L. (eds.): Geometric Reasoning. MIT Press, Cambridge (1988)
Ligozat, G.: Qualitative Spatial and Temporal Reasoning. Wiley-ISTE, London (2011)
Pesant, G., Boyer, M.: Reasoning about solids using constraint logic programming. J. Autom. Reason. 22(3), 241–262 (1999)
Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. KR 92, 165–176 (1992)
Sato, T.: A statistical learning method for logic programs with distribution semantics. In: The 12th International Conference on Logic Programming (ICLP 1995) (1995)
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 2015
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
Schultz, C., Bhatt, M.: A numerical optimisation based characterisation of spatial reasoning. In: Alferes, J.J., Bertossi, L., Governatori, G., Fodor, P., Roman, D. (eds.) RuleML 2016. LNCS, vol. 9718, pp. 199–207. Springer, Heidelberg (2016). doi:10.1007/978-3-319-42019-6_13
Van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM (JACM) 38(3), 619–649 (1991)
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)
Wallgrün, J.O.: Exploiting qualitative spatial reasoning for topological adjustment of spatial data. In: Proceedings of the 20th International Conference on Advances in Geographic Information Systems, pp. 229–238. ACM (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Schultz, C., Bhatt, M., Suchan, J. (2016). Probabilistic Spatial Reasoning in Constraint Logic Programming. In: Schockaert, S., Senellart, P. (eds) Scalable Uncertainty Management. SUM 2016. Lecture Notes in Computer Science(), vol 9858. Springer, Cham. https://doi.org/10.1007/978-3-319-45856-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-45856-4_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45855-7
Online ISBN: 978-3-319-45856-4
eBook Packages: Computer ScienceComputer Science (R0)