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Qualitative Spatial Representation and Reasoning: An Overview
 FUNDAMENTA INFORMATICAE
, 2001
"... The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning inclu ..."
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Cited by 264 (18 self)
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The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning including reasoning about spatial change. Finally there is a discussion of theoretical results and a glimpse of future work. The paper is a revised and condensed version of [33, 34].
Qualitative Spatial Representation and Reasoning
 An Overview”, Fundamenta Informaticae
, 2001
"... The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related ..."
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Cited by 71 (10 self)
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The need for spatial representations and spatial reasoning is ubiquitous in AI – from robot planning and navigation, to interpreting visual inputs, to understanding natural language – in all these cases the need to represent and reason about spatial aspects of the world is of key importance. Related fields of research, such as geographic information science
A Canonical Model of the Region Connection Calculus
 Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR98
, 1997
"... Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dim ..."
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Cited by 51 (5 self)
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Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dimension as used by the Region Connection Calculus. In this paper we present a canonical model which allows regions and relations between them to be represented as points of the topological space and information about their neighbourhoods. With this formalism we are able to prove that whenever a set of RCC8 formulas is consistent there exists a realization in any dimension, even when the regions are constrained to be (sets of) polytopes. For three and higher dimensional space this is also true for internally connected regions. Using the canonical model we give algorithms for generating consistent scenarios. 1 Introduction The Region Connection Calculus (RCC) is a topological approach t...
Efficient methods for qualitative spatial reasoning
 Proceedings of the 13th European Conference on Artificial Intelligence
, 1998
"... The theoretical properties of qualitative spatial reasoning in the RCC8 framework have been analyzed extensively. However, no empirical investigation has been made yet. Our experiments show that the adaption of the algorithms used for qualitative temporal reasoning can solve large RCC8 instances, ..."
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Cited by 51 (12 self)
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The theoretical properties of qualitative spatial reasoning in the RCC8 framework have been analyzed extensively. However, no empirical investigation has been made yet. Our experiments show that the adaption of the algorithms used for qualitative temporal reasoning can solve large RCC8 instances, even if they are in the phase transition region  provided that one uses the maximal tractable subsets of RCC8 that have been identified by us. In particular, we demonstrate that the orthogonal combination of heuristic methods is successful in solving almost all apparently hard instances in the phase transition region up to a certain size in reasonable time.
Qualitative direction calculi with arbitrary granularity
 In Proceedings of the 8th Pacific Rim International Conference on Artificial Intelligence
, 2004
"... Abstract. Binary direction relations between points in twodimensional space are the basis to any qualitative direction calculus. Previous calculi are only on a very low level of granularity. In this paper we propose a generalization of previous approaches which enables qualitative calculi with an a ..."
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Cited by 46 (8 self)
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Abstract. Binary direction relations between points in twodimensional space are the basis to any qualitative direction calculus. Previous calculi are only on a very low level of granularity. In this paper we propose a generalization of previous approaches which enables qualitative calculi with an arbitrary level of granularity. The resulting calculi are so powerful that they can even emulate a quantitative representation based on a coordinate system. We also propose a less powerful, purely qualitative version of the generalized calculus. We identify tractable subsets of the generalized calculus and describe some applications for which these calculi are useful. 1
Weak Composition for Qualitative Spatial and Temporal Reasoning. In: CP
, 2005
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Qualitative SpatioTemporal Reasoning with RCC8 and Allen's Interval Calculus: Computational Complexity
, 2002
"... There exist a number of qualitative constraint calculi that are used to represent and reason about temporal or spatial configurations. However, there are only very few approaches aiming to create a spatiotemporal constraint calculus. Similar to Bennett et al., we start with the spatial calculus RCC ..."
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Cited by 22 (1 self)
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There exist a number of qualitative constraint calculi that are used to represent and reason about temporal or spatial configurations. However, there are only very few approaches aiming to create a spatiotemporal constraint calculus. Similar to Bennett et al., we start with the spatial calculus RCC8 and Allen's interval calculus in order to construct a qualitative spatiotemporal calculus. As we will show, the basic calculus is NPcomplete, even if we only permit base relations. When adding the restriction that the size of the spatial regions persists over time, or that changes are continuous, the calculus becomes more useful, but the satisfiability problem appears to be much harder. Nevertheless, we are able to show that satisfiability is still in NP.
Combining Topological and Size Information for Spatial Reasoning
 Artificial Intelligence
, 2000
"... Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Regi ..."
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Cited by 21 (8 self)
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Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Region Connection Calculus RCC8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC8 relations is NPhard, but three large maximal tractable subclasses of RCC8, called b H8 , C8 and Q8 respectively, have been identied. We propose an O(n 3 ) time pathconsistency algorithm based on a novel technique for combining RCC8 relations and qualitative size relations forming a Point Algebra, where n is the number of spatial regions. This algorithm is correct and complete for deciding consistency when the topological relations are either in b H8 , C8 or Q8 , and has the same complexity as the best known method for deciding consistency...
Relation algebras and their application in temporal and spatial reasoning
 In: Artif. Intell. Rev
"... Abstract Qualitative temporal and spatial reasoning is in many cases based on binary relations such as before, after, starts, contains, contact, part of, and others derived from these by relational operators. The calculus of relation algebras is an equational formalism; it tells us which relations ..."
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Cited by 18 (3 self)
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Abstract Qualitative temporal and spatial reasoning is in many cases based on binary relations such as before, after, starts, contains, contact, part of, and others derived from these by relational operators. The calculus of relation algebras is an equational formalism; it tells us which relations must exist, given several basic operations, such as Boolean operations on relations, relational composition and converse. Each equation in the calculus corresponds to a theorem, and, for a situation where there are only nitely many relations, one can construct a composition table which can serve as a look up table for the relations involved. Since the calculus handles relations, no knowledge about the concrete geometrical objects is necessary. In this sense, relational calculus is pointless. Relation algebras were introduced into temporal reasoning by Allen [1] and into spatial reasoning by Egenhofer and Sharma
SOWL: A Framework for Handling Spatiotemporal Information
 in OWL 2.0.” in RuleML Europe, ser. Lecture Notes in Computer Science
, 2011
"... Abstract. We propose SOWL, an ontology for representing and reasoning over spatiotemporal information in OWL. Building upon well established standards of the semantic web (OWL 2.0, SWRL) SOWL enables representation of static as well as of dynamic information based on the 4Dfluents (or, equivalen ..."
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Cited by 16 (7 self)
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Abstract. We propose SOWL, an ontology for representing and reasoning over spatiotemporal information in OWL. Building upon well established standards of the semantic web (OWL 2.0, SWRL) SOWL enables representation of static as well as of dynamic information based on the 4Dfluents (or, equivalently, on the Nary) approach. Both RCC8 topological and coneshaped directional relations are integrated in SOWL. Representing both qualitative temporal and spatial information (i.e., information whose temporal or spatial extents are unknown such as “leftof ” for spatial and “before ” for temporal relations) in addition to quantitative information (i.e., where temporal and spatial information is defined precisely) is a distinctive feature of SOWL. The SOWL reasoner is capable of inferring new relations and checking their consistency, while retaining soundness, completeness, and tractability over the supported sets of relations. 1