Book ChapterDOI
Reasoning about ordering
Christoph Schlieder
- pp 341-349
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TLDR
A system of line segment relations which generalizes Allen's system of interval relations to two dimensions is introduced and it is shown that this generalization differs in interesting properties from the generalizations based on topological relations which have been proposed so far.Abstract:
Ordering information is a special type of spatial information that derives from the linear, planar or spatial ordering of points. A definition of ordering information in terms of the orientation of simplexes is used in this paper to introduce a system of line segment relations which generalizes Allen's system of interval relations to two dimensions. It shows that this generalization differs in interesting properties from the generalizations based on topological relations which have been proposed so far. The conceptual neighborhood structure of the line segment relations provides the foundation of ordering information reasoning. This is illustrated with an example from motion planning. Finally, the problem of representing ordering information is addressed. In that context the cell complex representation of Frank and Kuhn is compared with the approach presented here.read more
Citations
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Journal ArticleDOI
Qualitative Spatial Representation and Reasoning: An Overview
TL;DR: The paper is a overview of the major qualitative spatial representation and reasoning techniques including ontological aspects, topology, distance, orientation and shape, and qualitative spatial reasoning including reasoning about spatial change.
Book ChapterDOI
Qualitative spatial representation and reasoning
Anthony G. Cohn,Jochen Renz +1 more
TL;DR: 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.
Book ChapterDOI
Qualitative Spatial Representation and Reasoning Techniques
TL;DR: The state of the art in Qualitative Spatial Reasoning is surveyed, covering representation and reasoning issues as well as pointing to some application areas.
Proceedings Article
Qualitative spatial reasoning about line segments
TL;DR: 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.
Book ChapterDOI
Calculi for Qualitative Spatial Reasoning
TL;DR: This paper lays out a guide to the issues involved and surveys what has been achieved on qualitative spatial reasoning, providing pointers to the literature where full technical details may be found.
References
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Journal Article
Maintaining knowledge about temporal intervals
TL;DR: An interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation, which is notable in offering a delicate balance between space and time.
Journal ArticleDOI
Maintaining knowledge about temporal intervals
TL;DR: In this paper, an interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation, which is notable in offering a delicate balance between time and space.
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TL;DR: An interval logic for reasoning about space is described, which supports a simpler ontology, has fewer functions and relations, yet does not su er in terms of its useful expressiveness.
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Point-set topological spatial relations
TL;DR: A novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets, and it is shown that these relations correspond to some of the standard set theoretical andTopological spatial Relations between sets such as equality, disjointness and containment in the interior.
Journal ArticleDOI
Temporal reasoning based on semi-intervals
TL;DR: A generalization of Allen's interval-based approach to temporal reasoning is presented and the notion of ‘conceptual neighborhood’ of qualitative relations between events is central to the presented approach, using semi-intervals rather than intervals as the basic units of knowledge.