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144
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 51 (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.
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 50 (16 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
Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis
 In Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI99
, 1999
"... We present a general method for proving tractability of reasoning over disjunctions of jointly exhaustive and pairwise disjoint relations. Examples of these kinds of relations are Allen's temporal interval relations and their spatial counterpart, the RCC8 relations by Randell, Cui, and Cohn. Ap ..."
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Cited by 48 (15 self)
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We present a general method for proving tractability of reasoning over disjunctions of jointly exhaustive and pairwise disjoint relations. Examples of these kinds of relations are Allen's temporal interval relations and their spatial counterpart, the RCC8 relations by Randell, Cui, and Cohn. Applying this method does not require detailed knowledge about the considered relations; instead, it is rather sufficient to have a subset of the considered set of relations for which pathconsistency is known to decide consistency. Using this method, we give a complete classification of tractability of reasoning over RCC8 by identifying two large new maximal tractable subsets and show that these two subsets together with b H 8 , the already known maximal tractable subset, are the only such sets for RCC8 that contain all base relations. We also apply our method to Allen's interval algebra and derive the known maximal tractable subset. 1 Introduction In qualitative spatial and temporal reasoning,...
Qualitative direction calculi with arbitrary granularity
 In Proceedings of the 8th Pacific Rim International Conference on Artificial Intelligence
, 2004
"... Abstract. Binary direction relations between points in twodimensional space are the basis to any qualitative direction calculus. Previous calculi are only on a very low level of granularity. In this paper we propose a generalization of previous approaches which enables qualitative calculi with an a ..."
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Cited by 46 (8 self)
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Abstract. Binary direction relations between points in twodimensional space are the basis to any qualitative direction calculus. Previous calculi are only on a very low level of granularity. In this paper we propose a generalization of previous approaches which enables qualitative calculi with an arbitrary level of granularity. The resulting calculi are so powerful that they can even emulate a quantitative representation based on a coordinate system. We also propose a less powerful, purely qualitative version of the generalized calculus. We identify tractable subsets of the generalized calculus and describe some applications for which these calculi are useful. 1
Relation algebras in qualitative spatial reasoning
 Fundamenta Informaticae
, 1999
"... The formalization of the “part – of ” relationship goes back to the mereology of S. Le´sniewski, subsequently taken up by Leonard & Goodman (1940), and Clarke (1981). In this paper we investigate relation algebras obtained from different notions of “part–of”, respectively, “connectedness” in var ..."
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Cited by 39 (14 self)
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The formalization of the “part – of ” relationship goes back to the mereology of S. Le´sniewski, subsequently taken up by Leonard & Goodman (1940), and Clarke (1981). In this paper we investigate relation algebras obtained from different notions of “part–of”, respectively, “connectedness” in various domains. We obtain minimal models for the relational part of mereology in a general setting, and when the underlying set is an atomless Boolean algebra. 1
Weak Composition for Qualitative Spatial and Temporal Reasoning. In: CP
, 2005
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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 (14 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
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 29 (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...
A Categorical Axiomatisation of RegionBased Geometry
, 2001
"... . Region Based Geometry (RBG) is an axiomatic theory of qualitative congurations of spatial regions. It is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. Whereas in Tarski's theory the combination of mereological and ..."
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Cited by 27 (8 self)
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. Region Based Geometry (RBG) is an axiomatic theory of qualitative congurations of spatial regions. It is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. Whereas in Tarski's theory the combination of mereological and geometrical axioms involves set theory, in RBG the interface is achieved by purely 1storder axioms. This means that the elementary sublanguage of RBG is extremely expressive, supporting inferences involving both mereological and geometrical concepts. Categoricity of the RBG axioms is proved: all models are isomorphic to a standard interpretation in terms of Cartesian spaces over R. 1. Introduction Many researchers in the eld of Qualitative Spatial Reasoning (QSR) have argued that it is useful to have representations in which spatial regions are the basic entities [10, 8]. This ontology contrasts with the approach of classical geometry, where lines, surfaces and regions are typically thought of as ...
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.