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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 204 (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].
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 50 (7 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
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 45 (15 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 Axiom System for Polygonal Mereotopology of the Real Plane
, 1997
"... This paper presents a calculus for mereotopological reasoning in which twodimensional spatial regions are treated as primitive entities. A first order predicate language L with a distinguished unary predicate c(x), functionsymbols +; : and \Gamma and constants 0 and 1 is defined. An interpretation ..."
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Cited by 44 (5 self)
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This paper presents a calculus for mereotopological reasoning in which twodimensional spatial regions are treated as primitive entities. A first order predicate language L with a distinguished unary predicate c(x), functionsymbols +; : and \Gamma and constants 0 and 1 is defined. An interpretation R for L is provided in which polygonal open subsets of the real plane serve as elements of the domain. Under this interpretation the predicate c(x) is read as "region x is connected" and the functionsymbols and constants are given their meaning in terms of a Boolean algebra of polygons. We give an alternative interpretation S based on the real closed plane which turns out to be isomorphic to R. A set of axioms and a rule of inference are introduced. We prove the soundness and completeness of the calculus with respect to the given interpretation.
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 44 (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...
RegionBased Qualitative Geometry
, 2000
"... We present a highly expressive logical language for describing qualitative configurations of spatial regions. We call the theory Region Based Geometry (RBG). Our axiomatisation is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as pri ..."
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Cited by 35 (15 self)
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We present a highly expressive logical language for describing qualitative configurations of spatial regions. We call the theory Region Based Geometry (RBG). Our axiomatisation is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We show that our theory is categorical: all models are isomorphic to a classical interpretation in terms of Cartesian spaces over R. We investigate
Undecidability of Plane Polygonal Mereotopology
 Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR98
, 1998
"... This paper presents a mereotopological model of polygonal regions of the Euclidean plane and an undecidability proof of its firstorder theory. Restricted to the primitive operations the model is a Boolean algebra. Its single primitive predicate defines simple polygons as the topologically simplest p ..."
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Cited by 21 (0 self)
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This paper presents a mereotopological model of polygonal regions of the Euclidean plane and an undecidability proof of its firstorder theory. Restricted to the primitive operations the model is a Boolean algebra. Its single primitive predicate defines simple polygons as the topologically simplest polygonal regions. It turns out that both the relations usually provided by mereotopologies and more subtle topological relations are elementarily definable in the model. Using these relations, Post's correspondence problem, known as undecidable, can be reduced to the decision problem of the model. 1 Introduction Formalizing commonsense concepts of space has received much attention both in the philosophical literature and in recent AI research. Mereotopological theories as well as most calculi for spatial reasoning deal with spatial regions, i.e. the parts of space occupied by physical bodies, and their topological relations as intuitive concepts of our commonsense space. Whereas mereotopolo...
Expressivity in Polygonal, Plane Mereotopology
 JOURNAL OF SYMBOLIC LOGIC
, 1998
"... In recent years, there has been renewed interest in the development of formal languages for describing mereological (partwhole) and topological relationships between objects in space. Typically, the nonlogical primitives of these languages are properties and relations such as `x is connected' ..."
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Cited by 18 (2 self)
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In recent years, there has been renewed interest in the development of formal languages for describing mereological (partwhole) and topological relationships between objects in space. Typically, the nonlogical primitives of these languages are properties and relations such as `x is connected' or `x is a part of y', and the entities over which their variables range are, accordingly, not points, but regions: spatial entities other than regions are admitted, if at all, only as logical constructs of regions. This paper considers two ørstorder mereotopological languages, and investigates their expressive power. It turns out that these languages, notwithstanding the simplicity of their primitives, are surprisingly expressive. In particular, it is shown that inønitary versions of these languages are adequate to express (in a sense made precise below) all topological relations over the domain of polygons in the closed plane.
Connection Relations in Mereotopology
, 1998
"... We provide a modeltheoretic framework for investigating and comparing a variety of mereotopological theories with respect to (i) the intended interpretation of their connection primitives, and (ii) the composition of their intended domains (e.g., whether or not they allow for boundary elements). ..."
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Cited by 18 (3 self)
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We provide a modeltheoretic framework for investigating and comparing a variety of mereotopological theories with respect to (i) the intended interpretation of their connection primitives, and (ii) the composition of their intended domains (e.g., whether or not they allow for boundary elements).
Logical Patterns in Space
 University of Amsterdam
, 1999
"... In this paper, we revive the topological interpretation of modal logic, turning it into a general language of patterns in space. In particular, we define a notion of bisimulation for topological models that compares different visual scenes. We refine the comparison by introducing EhrenfeuchtFra ..."
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Cited by 18 (5 self)
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In this paper, we revive the topological interpretation of modal logic, turning it into a general language of patterns in space. In particular, we define a notion of bisimulation for topological models that compares different visual scenes. We refine the comparison by introducing EhrenfeuchtFra iss'e style games between patterns in space. Finally, we consider spatial languages of increased logical power in the direction of geometry. Also, Intelligent Sensory Information Systems, University of Amsterdam 1 Contents 1 Reasoning about Space 3 2 Topological Structure: a Modal Approach 4 2.1 The topological view of space . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Topological spaces . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Special properties of topological spaces . . . . . . . . . . . 6 2.1.3 Structure preserving mappings . . . . . . . . . . . . . . . 7 3 Basic Modal Logic of Space 8 3.1 Topological language and semantics . . . . . . . . . . . . . . . . 8 3.2 Topologi...