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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 representation theorem for Boolean contact algebras.
 Theoretical Computer Science
, 2005
"... Abstract We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [23] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T 1 spaces. ..."
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Cited by 48 (16 self)
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Abstract We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [23] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T 1 spaces.
Qualitative SpatioTemporal Representation and Reasoning: A Computational Perspective
 Exploring Artifitial Intelligence in the New Millenium
, 2001
"... this paper argues for the rich world of representation that lies between these two extremes." Levesque and Brachman (1985) 1 Introduction Time and space belong to those few fundamental concepts that always puzzled scholars from almost all scientific disciplines, gave endless themes to science ..."
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Cited by 39 (12 self)
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this paper argues for the rich world of representation that lies between these two extremes." Levesque and Brachman (1985) 1 Introduction Time and space belong to those few fundamental concepts that always puzzled scholars from almost all scientific disciplines, gave endless themes to science fiction writers, and were of vital concern to our everyday life and commonsense reasoning. So whatever approach to AI one takes [ Russell and Norvig, 1995 ] , temporal and spatial representation and reasoning will always be among its most important ingredients (cf. [ Hayes, 1985 ] ). Knowledge representation (KR) has been quite successful in dealing separately with both time and space. The spectrum of formalisms in use ranges from relatively simple temporal and spatial databases, in which data are indexed by temporal and/or spatial parameters (see e.g. [ Srefik, 1995; Worboys, 1995 ] ), to much more sophisticated numerical methods developed in computational geom
MODAL LOGICS OF TOPOLOGICAL RELATIONS
 ACCEPTED FOR PUBLICATION IN LOGICAL METHODS IN COMPUTER SCIENCE
, 2006
"... Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we int ..."
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Cited by 24 (6 self)
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Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham’s modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the EgenhoferFranzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the twovariable fragment of firstorder logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to Π 1 1hard, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity.
A Proximity Approach to Some RegionBased Theories of Space
, 2002
"... This paper is a continuation of [41]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to... ..."
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Cited by 24 (14 self)
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This paper is a continuation of [41]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to...
Spatial Relations Between Indeterminate Regions
 INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
, 2000
"... Systems of relations between regions are an important aspect of formal theories of spatial data. Examples of such relations are partof, partially overlapping, and disjoint. One particular family of systems is that based on the RegionConnection Calculus (RCC). These systems of relations were or ..."
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Cited by 14 (1 self)
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Systems of relations between regions are an important aspect of formal theories of spatial data. Examples of such relations are partof, partially overlapping, and disjoint. One particular family of systems is that based on the RegionConnection Calculus (RCC). These systems of relations were originally formulated for ideal regions, not subject to imperfections such as vagueness or indeterminacy. This paper presents two new methods for extending the relations based on the RCC from crisp regions to indeterminate regions. As a formal context for these two methods we develop an algebraic approach to spatial indeterminacy using Łukasiewicz algebras. This algebraic approach provides a generalisation of the "eggyolk" model of indeterminate regions. The two extension methods which we develop are proved to be equivalent. In particular, it is shown that it is possible to dene partof in terms of connection in the indeterminate case. This generalises a wellknown result about cris...
A Note on Proximity Spaces and Connection Based Mereology
, 2001
"... Representation theorems for systems of regions have been of interest for some time, and various contexts have been used for this purpose: Mormann [17] has demonstrated the fruitfulness of the methods of continuous lattices to obtain a topological representation theorem for his formalisation of White ..."
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Cited by 12 (8 self)
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Representation theorems for systems of regions have been of interest for some time, and various contexts have been used for this purpose: Mormann [17] has demonstrated the fruitfulness of the methods of continuous lattices to obtain a topological representation theorem for his formalisation of Whiteheadian ontological theory of space; similar results have been obtained by Roeper [20]. In this note, we prove a topological representation theorem for a connection based class of systems, using methods and tools from the theory of proximity spaces. The key novelty is a new proximity semantics for connection relations.
Continuous Transitions in Mereotopology
, 2001
"... Continuity from a qualitative perspective is different from both the philosophical and mathematical view of continuity. We explore different intuitive notions of spatiotemporal continuity. We present a general formal framework for continuity and continuous transitions in mereotopology for spa ..."
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Cited by 11 (8 self)
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Continuity from a qualitative perspective is different from both the philosophical and mathematical view of continuity. We explore different intuitive notions of spatiotemporal continuity. We present a general formal framework for continuity and continuous transitions in mereotopology for spatiotemporal histories and thus sketch the correctness of the conceptual neighbourhood for the qualitative spatial representation language RCC8.
AXIOMS, ALGEBRAS, AND TOPOLOGY
"... This work explores the interconnections between a number of different perspectives on the formalisation of space. We begin with an informal discussion of the intuitions that motivate these formal representations. ..."
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Cited by 9 (0 self)
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This work explores the interconnections between a number of different perspectives on the formalisation of space. We begin with an informal discussion of the intuitions that motivate these formal representations.
Construction of Boolean Contact Algebras
 AI Communications
, 2004
"... We consider Boolean algebras endowed with a contact relation which are abstractions of Boolean algebras of regular closed sets together with Whitehead's connection relation [17], in which two nonempty regular closed sets are connected if they have a nonempty intersection. These are standard e ..."
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Cited by 8 (7 self)
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We consider Boolean algebras endowed with a contact relation which are abstractions of Boolean algebras of regular closed sets together with Whitehead's connection relation [17], in which two nonempty regular closed sets are connected if they have a nonempty intersection. These are standard examples for structures used in qualitative reasoning, mereotopology, and proximity theory. We exhibit various methods how such algebras can be constructed and give several nonstandard examples, the most striking one being a countable model of the Region Connection Calculus in which every proper region has infinitely many holes. 1