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Probabilistic Spatial Reasoning in Constraint Logic Programming

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Book cover Scalable Uncertainty Management (SUM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9858))

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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.

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Notes

  1. 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. 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. 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. 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. 5.

    For brevity we do not list all of the spatial constraint definitions here, and instead we refer readers to [3, 23].

  6. 6.

    www.freecadweb.org.

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Author information

Authors and Affiliations

  1. University of Münster, Münster, Germany

    Carl Schultz

  2. University of Bremen, Bremen, Germany

    Mehul Bhatt & Jakob Suchan

  3. The DesignSpace Group, Bremen, Germany

    Carl Schultz, Mehul Bhatt & Jakob Suchan

Authors
  1. Carl Schultz
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  2. Mehul Bhatt
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  3. Jakob Suchan
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Correspondence to Carl Schultz .

Editor information

Editors and Affiliations

  1. Cardiff University , Cardiff, United Kingdom

    Steven Schockaert

  2. Télécom ParisTech , Paris, Paris, France

    Pierre Senellart

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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

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  • DOI: https://doi.org/10.1007/978-3-319-45856-4_20

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-45856-4

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