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On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
TLDR
It is proved that reasoning is NP-complete in general and identified a maximal tractable subset of the relations in RCC-8 that contains all base relations and shows that for this subset path-consistency is sufficient for deciding consistency. Expand
Qualitative Spatial Reasoning Using Constraint Calculi
Qualitative Spatial Reasoning with Topological Information
  • Jochen Renz
  • Mathematics, Computer Science
  • Lecture Notes in Computer Science
  • 27 February 2002
TLDR
This work Enumeration of the Relations of the Maximal Tractable Subsets of RCC-8 and Empirical Evaluation of Reasoning with R CC-8 shows positive results in terms of tractability and representation. Expand
Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis
  • Jochen Renz
  • Mathematics, Computer Science
  • IJCAI
  • 31 July 1999
TLDR
A general method for proving tractability of reasoning over disjunctions of jointly exhaustive and pairwise disjoint relations of Allen's temporal interval relations and their spatial counterpart, the R.CC8 relations by Randell, Cui, and Colin is presented. Expand
What Is a Qualitative Calculus? A General Framework
TLDR
It is shown that the natural algebraic object governing this kind of calculus is a non-associative algebra (in the sense of Maddux), and that the notion of weak representation is the right notion for describing most basic properties. Expand
Qualitative Spatial Representation and Reasoning
TLDR
The challenge of qualitative spatial reasoning (QSR) is to provide calculi that allow a machine to represent and reason with spatial entities without resort to the traditional quantitative techniques prevalent in, for example, computer graphics or computer vision communities. Expand
Efficient Methods for Qualitative Spatial Reasoning
TLDR
The experiments show that the adaption of the algorithms used for qualitative temporal reasoning can solve large RCC-8 instances, even if they are in the phase transition region - provided that one uses the maximal tractable subsets of R CC-8 that have been identified by us. Expand
Weak Composition for Qualitative Spatial and Temporal Reasoning
TLDR
It turns out that the most important property of a qualitative calculus is not whether weak composition is equivalent to composition, but whether the relations are closed under constraints, and a new concept for qualitative relations, the "closure under constraints". Expand
Qualitative Spatial Reasoning about Line Segments
TLDR
A novel approach for dealing with intrinsic orientation information by specifying qualitative relations between oriented line segments, the simplest possible spatial entities being extended and having an intrinsic direction is presented. Expand
A Canonical Model of the Region Connection Calculus
  • Jochen Renz
  • Computer Science, Mathematics
  • J. Appl. Non Class. Logics
  • 26 November 1997
TLDR
A canonical model of R CC-8 is developed which allows a simple representation of regions with respect to a set of RCC-8 constraints, and enables us to generate realizations in any dimension d = 1. Expand
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