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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 261 (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].
On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
 Artificial Intelligence
, 1997
"... The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus&quo ..."
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Cited by 141 (23 self)
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The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. We extend Bennett's encoding of RCC8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC8 that contains all base relations. Further, we show that for this subset pathconsistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the socalled Region Connecti...
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 67 (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
Spatial Reasoning with Topological Information
 Ph.D. thesis, Institut fur Informatik, AlbertLudwigsUniversitat Freiburg
, 1998
"... . This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the re ..."
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Cited by 60 (2 self)
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. This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the required dimension of the applied space. Further, it includes computational issues, e.g., how hard is it to reason with the calculus and are there efficient algorithms. Finally, we also address cognitive issues, i.e., is the calculus cognitively adequate. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. Different aspects of space can be treated in a qualitative way. Among others there are approaches considering orientation, distance, shape, topology, and combinations of these. A summary o...
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 52 (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.
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...
Foundations of spatioterminological reasoning with description logics
 In Cohn et al
"... This paper presents a method for reasoning about spatial objects and their qualitative spatial relationships. In contrast to existing work, which mainly focusses on reasoning about qualitative spatial relations alone, we integrate quantitative and qualitative information with terminological reasonin ..."
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Cited by 51 (17 self)
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This paper presents a method for reasoning about spatial objects and their qualitative spatial relationships. In contrast to existing work, which mainly focusses on reasoning about qualitative spatial relations alone, we integrate quantitative and qualitative information with terminological reasoning. For spatioterminological reasoning we present the description logic ALCRP(D) and define an appropriate concrete domain D for polygons. The theory is motivated as a basis for knowledge representation and query processing in the domain of deductive geographic information systems. 1
A Complete Classification of Tractability in RCC5
 Journal of Artificial Intelligence Research
, 1997
"... We investigate the computational properties of the spatial algebra RCC5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC5 is known to be NPcomplete but not much is known about its approximately four billion subclasses. We provide a compl ..."
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Cited by 30 (7 self)
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We investigate the computational properties of the spatial algebra RCC5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC5 is known to be NPcomplete but not much is known about its approximately four billion subclasses. We provide a complete classification of satisfiability for all these subclasses into polynomial and NPcomplete respectively. In the process, we identify all maximal tractable subalgebras which are four in total. 1. Introduction Qualitative spatial reasoning has received a constantly increasing amount of interest in the literature. The main reason for this is, probably, that spatial reasoning has proved to be applicable to realworld problems in, for example, geographical database systems (Egenhofer, 1991; Grigni, Papadias, & Papadimitriou, 1995) and molecular biology (Cui, 1994). In both these applications, the size of the problem instances can be huge, so the complexity of problems and algorithms is a highly...
Reasoning about Categories in Conceptual Spaces
 In Proceedings of the Fourteenth International Joint Conference of Artificial Intelligence
, 2001
"... Understanding the process of categorization is a primary research goal in artificial intelligence. The conceptual space framework provides a flexible approach to modeling contextsensitive categorization via a geometrical representation designed for modeling and managing concepts. In this paper we s ..."
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Cited by 22 (2 self)
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Understanding the process of categorization is a primary research goal in artificial intelligence. The conceptual space framework provides a flexible approach to modeling contextsensitive categorization via a geometrical representation designed for modeling and managing concepts. In this paper we show how algorithms developed in computational geometry, and the Region Connection Calculus can be used to model important aspects of categorization in conceptual spaces. In particular, we demonstrate the feasibility of using existing geometric algorithms to build and manage categories in conceptual spaces, and we show how the Region Connection Calculus can be used to reason about categories and other conceptual regions. 1
Spatial Logic and the Complexity of Diagrammatic Reasoning
 MACHINE GRAPHICS AND VISION
, 1997
"... Researchers have sought to explain the observed "efficacy" of diagrammatic reasoning (DR) via the notions of "limited abstraction" and inexpressivity [17, 20]. We argue that application of the concepts of computational complexity to systems of diagrammatic representation is neces ..."
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Cited by 22 (2 self)
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Researchers have sought to explain the observed "efficacy" of diagrammatic reasoning (DR) via the notions of "limited abstraction" and inexpressivity [17, 20]. We argue that application of the concepts of computational complexity to systems of diagrammatic representation is necessary for the evaluation of precise claims about their efficacy. We show here how to give such an analysis. Centrally, we claim that recent formal analyses of diagrammatic representations (DRs) (eg: [14]) fail to account for the ways in which they employ spatial relations in their representational work. This focus raises some problems for the expressive power of graphical systems, related to the topological and geometrical constraints of the medium. A further idea is that some diagrammatic reasoning may be analysed as a variety of topological inference [15]. In particular, we show how reasoning in some diagrammatic systems is of polynomial complexity, while reasoning in others is NP hard. A simple case study i...