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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 182 (17 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 Equivalence of Topological Relations
 International Journal of Geographical Information Systems
, 1995
"... Abstract. Analysis of global geographic phenomena requires nonplanar models. In the past, models for topological relations have focused either on a twodimensional or a threedimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the twodimensio ..."
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Cited by 113 (13 self)
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Abstract. Analysis of global geographic phenomena requires nonplanar models. In the past, models for topological relations have focused either on a twodimensional or a threedimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the twodimensional planar case, the eight binary topological relations between spatial regions are well known from the 9intersection model. This paper systematically develops the binary topological relations that can be realized on the surface of a sphere. Between two regions on the sphere there are three binary relations that cannot be realized in the plane. These relations complete the conceptual neighborhood graph of the eight planar topological relations in a regular fashion, providing evidence for a regularity of the underlying mathematical model. The analysis of the algebraic compositions of spherical topological relations indicates that spherical topological reasoning often provides fewer ambiguities than planar topological reasoning. Finally, a comparison with the relations that can be realized for onedimensional, ordered cycles draws parallels to the spherical topological relations. 1
Qualitative Spatial Representation and Reasoning with the Region Connection Calculus
 PROCEEDINGS OF THE DIMACS INTERNATIONAL WORKSHOP ON GRAPH DRAWING, 1994. LECTURE NOTES IN COMPUTER SCIENCE
, 1997
"... This paper surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show ..."
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Cited by 81 (3 self)
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This paper surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distinguish between convex and a variety of concave shapes and there is also an extension which handles regions with uncertain boundaries. We also present a variety of reasoning techniques, both for static and dynamic situations. A number of possible application areas are briefly mentioned.
A Theory of Granular Partitions
, 2001
"... This paper presents an application of the theory of granular partitions proposed in (Smith and Brogaard, to appear), (Smith and Bittner 2001) to the phenomenon of vagueness. We understand vagueness as a semantic property of names and predicates. This is in contrast to those views which hold that the ..."
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Cited by 72 (34 self)
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This paper presents an application of the theory of granular partitions proposed in (Smith and Brogaard, to appear), (Smith and Bittner 2001) to the phenomenon of vagueness. We understand vagueness as a semantic property of names and predicates. This is in contrast to those views which hold that there are intrinsically vague objects or attributes in reality and thus conceive vagueness in a de re fashion. All entities are crisp, on de dicto view here defended, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We show that the theory of granular partitions provides a general framework within which we can understand the relation between terms and concepts on the one hand and their multiple referents or extensions on the other, and we show how it might be possible to formulate within this framework a solution to the Sorites paradox. 1.
Parts, Wholes, and PartWhole Relations: The Prospects of Mereotopology
 Data and Knowledge Engineering
, 1996
"... INTRODUCTION This is a brief overview of formal theories concerned with the study of the notions of (and the relations between) parts and wholes. The guiding idea is that we can distinguish between a theory of parthood (mereology) and a theory of wholeness (holology, which is essentially afforded b ..."
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Cited by 62 (13 self)
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INTRODUCTION This is a brief overview of formal theories concerned with the study of the notions of (and the relations between) parts and wholes. The guiding idea is that we can distinguish between a theory of parthood (mereology) and a theory of wholeness (holology, which is essentially afforded by topology), and the main question examined is how these two theories can be combined to obtain a unified theory of parts and wholes. We examine various nonequivalent ways of pursuing this task, mainly with reference to its relevance to spatiotemporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) theories; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory subsuming mereology. This is done in Sections 4 through 6. We also consider some more speculative strategies and directions for further research. First, however, we begin with some preliminary outline of
Representing And Reasoning With Qualitative Spatial Relations About Regions
"... . This chapter surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and ..."
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Cited by 50 (5 self)
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. This chapter surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distinguish between convex and a variety of concave shapes and there is also an extension which handles regions with uncertain boundaries. We also present a variety of reasoning techniques, both for static and dynamic situations. A number of possible application areas are briefly mentioned. 1. Introduction Qualitative Reasoning (QR) has now become a mature subfield of AI as its tenth annual international workshop, several books (e.g. (Weld and De Kleer 1990, Faltings and Struss 1992)) and a wealth of conference and journal publications testify. QR tries to make explicit our everyday commonsense kno...
A Connection Based Approach to Commonsense Topological Description and Reasoning
, 1995
"... The standard mathematical approaches to topology, pointset topology and algebraic topology, treat points as the fundamental, undefined entities, and construct extended spaces as sets of points with additional structure imposed on them. Pointset topology in particular generalises the concept of ..."
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Cited by 49 (9 self)
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The standard mathematical approaches to topology, pointset topology and algebraic topology, treat points as the fundamental, undefined entities, and construct extended spaces as sets of points with additional structure imposed on them. Pointset topology in particular generalises the concept of a `space' far beyond its intuitive meaning. Even algebraic topology, which concentrates on spaces built out of `cells' topologically equivalent to ndimensional discs, concerns itself chiefly with rather abstract reasoning concerning the association of algebraic structures with particular spaces, rather than the kind of topological reasoning which is required in everyday life, or which might illuminate the metaphorical use of topological concepts such as `connection' and `boundary'. This paper explores an alternative to these approaches, RCC theory, which takes extended spaces (`regions') rather than points as fundamental. A single relation, C (x; y) (read `Region x connects with reg...
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 46 (6 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
Boolean Connection Algebras: A New Approach to the RegionConnection Calculus
 Artificial Intelligence
, 1999
"... The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and prove ..."
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Cited by 43 (7 self)
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The RegionConnection Calculus (RCC) is a well established formal system for qualitative spatial reasoning. It provides an axiomatization of space which takes regions as primitive, rather than as constructions from sets of points. The paper introduces boolean connection algebras (BCAs), and proves that these structures are equivalent to models of the RCC axioms. BCAs permit a wealth of results from the theory of lattices and boolean algebras to be applied to RCC. This is demonstrated by two theorems which provide constructions for BCAs from suitable distributive lattices. It is already well known that regular connected topological spaces yield models of RCC, but the theorems in this paper substantially generalize this result. Additionally, the lattice theoretic techniques used provide the first proof of this result which does not depend on the existence of points in regions. Keywords: RegionConnection Calculus, Qualitative Spatial Reasoning, Boolean Connection Algebra, Mer...
Imprecision in Finite Resolution Spatial Data
 GeoInformatica
, 1997
"... An important component of spatial data quality is the imprecision resulting from the resolution at which data are represented. Current research on topics such as spatial data integration and generalisation needs to be wellfounded on a theory of multiresolution. This paper provides a formal framewo ..."
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Cited by 43 (7 self)
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An important component of spatial data quality is the imprecision resulting from the resolution at which data are represented. Current research on topics such as spatial data integration and generalisation needs to be wellfounded on a theory of multiresolution. This paper provides a formal framework for treating the notion of resolution and multiresolution in geographic spaces. It goes further to develop an approach to reasoning with imprecision about spatial entities and relationships resulting from finite resolution representations. The approach is similar to aspects of rough and fuzzy set theories. The paper concludes by providing the beginnings of a geometry of vague spatial entities and relationships. Keywords: uncertainty, vagueness, rough set, fuzzy set, resolution, spatial reasoning, data quality 1. Introduction The notion of spatial resolution is fundamental to many aspects of the representation of spatial data, and a proper formulation of a multiresolution data model is...