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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 179 (16 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].
Using Orientation Information for Qualitative Spatial Reasoning
 Theories and Methods of SpatioTemporal Reasoning in Geographic Space, LNCS 639, SpringerVerlag
, 1992
"... Abstract. A new approach to representing qualitative spatial knowledge and to spatial reasoning is presented. This approach is motivated by cognitive considerations and is based on relative orientation information about spatial environments. The approach aims at exploiting properties of physical spa ..."
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Cited by 164 (8 self)
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Abstract. A new approach to representing qualitative spatial knowledge and to spatial reasoning is presented. This approach is motivated by cognitive considerations and is based on relative orientation information about spatial environments. The approach aims at exploiting properties of physical space which surface when the spatial knowledge is structured according to conceptual neighborhood of spatial relations. The paper introduces the notion of conceptual neighborhood and its relevance for qualitative temporal reasoning. The extension of the benefits to spatial reasoning is suggested. Several approaches to qualitative spatial reasoning are briefly reviewed. Differences between the temporal and the spatial domain are outlined. A way of transferring a qualitative temporal reasoning method to the spatial domain is proposed. The resulting neighborhoodoriented representation and reasoning approach is presented and illustrated. An example for an application of the approach is discussed. 1
Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen's Interval Algebra
 Journal of the ACM
, 1995
"... We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiabil ..."
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Cited by 161 (9 self)
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We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiability. Further, using an extensive machinegenerated case analysis, we show that the ORDHorn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. This work has been supported by the German Ministry for Research and Technology (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project. 1 1 Introduction Temporal information is often conveyed qualitatively by specifying the relative positions of time intervals such as ". . . point to the figure while explaining the performance of the system . . . "...
The `EggYolk' Representation Of Regions with Indeterminate Boundaries
, 1995
"... The paper proposes an approach to representing and reasoning about spatial regions with undetermined boundaries, using an adaptation of `RCCtheory', a regionbased system for representing qualitative spatial relations developed over the last few years (Randell, Cui and Cohn 1992, Cohn, Randell and C ..."
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Cited by 122 (11 self)
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The paper proposes an approach to representing and reasoning about spatial regions with undetermined boundaries, using an adaptation of `RCCtheory', a regionbased system for representing qualitative spatial relations developed over the last few years (Randell, Cui and Cohn 1992, Cohn, Randell and Cui 1994). The approach proposed is referred to as the `eggyolk' representation: a region with undetermined boundaries (a `vague region') is represented by a pair of concentric regions with determinate boundaries (`crisp regions'), which provide limits (not necessarily the tightest limits possible) on the range of indeterminacy. 1 Introduction The topic of this paper is how best to deal with vagueness in spatial representation and reasoning, particularly within the framework of `RCCtheory', (Randell, Cui and Cohn 1992, Cohn et al. 1994), which provides a representation of topological properties and relations in which regions rather than points are taken as primitive. We are concern...
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 114 (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
Topological Relations in the World of Minimum Bounding Rectangles: A Study with RTrees
, 1995
"... Recent developments in spatial relations have led to their use in numerous applications involving spatial databases. This paper is concerned with the retrieval of topological relations in Minimum Bounding Rectanglebased data structures. We study the topological information that Minimum Bounding Rec ..."
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Cited by 99 (30 self)
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Recent developments in spatial relations have led to their use in numerous applications involving spatial databases. This paper is concerned with the retrieval of topological relations in Minimum Bounding Rectanglebased data structures. We study the topological information that Minimum Bounding Rectangles convey about the actual objects they enclose, using the concept of projections. Then we apply the results to Rtrees and their variations, Rtrees and R*trees in order to minimise disk accesses for queries involving topological relations. We also investigate queries that involve complex spatial conditions in the form of disjunctions and conjunctions and we discuss possible extensions.
Qualitative Representation of Positional Information
 ARTIFICIAL INTELLIGENCE
, 1997
"... A framework for the qualitative representation of positional information in a twodimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flex ..."
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Cited by 91 (3 self)
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A framework for the qualitative representation of positional information in a twodimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flexible framework that accommodates various levels of granularity and scales of reasoning. Knowledge about position in largescale space is commonly represented by a combination of orientation and distance relations, which we express in a particular frame of reference between a primary object and a reference object. While the representation of orientation comes out to be more straightforward, the model for distances requires that qualitative distance symbols be mapped to geometric intervals in order to be compared; this is done by defining structure relations that are able to handle, among others, order of magnitude relations; the frame of reference with its three components (distance system, s...
Mereotopology: a theory of parts and boundaries
 Data & Knowledge Engineering
, 1996
"... The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes. to relations of contact and connectedness. to the concepts of surface, point, neighbourhood. and so on. The basis of the theory ..."
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Cited by 88 (19 self)
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The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes. to relations of contact and connectedness. to the concepts of surface, point, neighbourhood. and so on. The basis of the theory is mereology. the formal theory of part and whole, a theory which is shown to have a number of advantages. for ontological purposes. over standard treatments of topology in settheoretic terms. One central goal of the paper is to provide a rigorous formulation of B~ntano's thesis to the effect that a boundary can exist as a matter of necessity only as part of a whole of higher dimension of which it is the boundary. It concludes with a brief survey of current applications of mereotopology in areas such as naturallanguage analysis, geographic information systems, machine vision, naive physics, and database and knowledge engineering.
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...
Preferred mental models in qualitative spatial reasoning: A cognitive assessment of Allen's calculus
 In Proceedings of the Seventeenth Annual Conference of the Cognitive Science Society
, 1995
"... An experiment based on Allen's calculus and its transfer to qualitative spatial reasoning, was conducted. Subjects had to find a conclusion X r 3 Z that was consistent with the given premises X r 1 Y and Y r 2 Z. Implications of the obtained results are discussed with respect to the mental model the ..."
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Cited by 49 (17 self)
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An experiment based on Allen's calculus and its transfer to qualitative spatial reasoning, was conducted. Subjects had to find a conclusion X r 3 Z that was consistent with the given premises X r 1 Y and Y r 2 Z. Implications of the obtained results are discussed with respect to the mental model theory of spatial inference. The results support the assumption that there are preferred models when people solve spatial threeterm series problems. Although the subjects performed the task surprisingly well overall, there were significant differences in error rates between some of the tasks. They are discussed with respect to the subprocesses of model construction, model inspection, validation of the answer, and the interaction of these subprocesses.