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On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
 Artificial Intelligence
, 1997
"... The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus&quo ..."
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Cited by 144 (23 self)
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The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. We extend Bennett's encoding of RCC8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC8 that contains all base relations. Further, we show that for this subset pathconsistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the socalled Region Connecti...
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 Canonical Model of the Region Connection Calculus
 Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR98
, 1997
"... Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dim ..."
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Cited by 51 (5 self)
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Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dimension as used by the Region Connection Calculus. In this paper we present a canonical model which allows regions and relations between them to be represented as points of the topological space and information about their neighbourhoods. With this formalism we are able to prove that whenever a set of RCC8 formulas is consistent there exists a realization in any dimension, even when the regions are constrained to be (sets of) polytopes. For three and higher dimensional space this is also true for internally connected regions. Using the canonical model we give algorithms for generating consistent scenarios. 1 Introduction The Region Connection Calculus (RCC) is a topological approach t...
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
Qualitative Spatial Reasoning about Line Segments
 ECAI 2000. Proceedings of the 14th European Conference on Artifical Intelligence
, 2000
"... . Representing and reasoning about orientation information is an important aspect of qualitative spatial reasoning. We present a novel approach for dealing with intrinsic orientation information by specifying qualitative relations between oriented line segments, the simplest possible spatial entitie ..."
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Cited by 42 (12 self)
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. Representing and reasoning about orientation information is an important aspect of qualitative spatial reasoning. We present a novel approach for dealing with intrinsic orientation information by specifying qualitative relations between oriented line segments, the simplest possible spatial entities being extended and having an intrinsic direction. We identify a set of 24 atomic relations which form a relation algebra and for which we compute relational compositions based on their algebraic semantics. Reasoning over the full algebra turns out to be NPhard. Potential applications of the calculus are motivated with a small example which shows the reasoning capabilities of the dipole calculus using constraintbased reasoning methods. 1 Introduction Qualitative representation of space abstracts from the physical world and enables computers to make predictions about spatial relations, even when precise quantitative information is not available [2]. Different aspects of space can be repr...
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
GQR – A Fast Reasoner for Binary Qualitative Constraint Calculi
"... GQR (Generic Qualitative Reasoner) is a solver for binary qualitative constraint networks. GQR takes a calculus description and one or more constraint networks as input, and tries to solve the networks using the path consistency method and (heuristic) backtracking. In contrast to specialized reasone ..."
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Cited by 26 (8 self)
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GQR (Generic Qualitative Reasoner) is a solver for binary qualitative constraint networks. GQR takes a calculus description and one or more constraint networks as input, and tries to solve the networks using the path consistency method and (heuristic) backtracking. In contrast to specialized reasoners, it offers reasoning services for different qualitative calculi, which means that these calculi are not hardcoded into the reasoner. Currently, GQR supports arbitrary binary constraint calculi developed for spatial and temporal reasoning, such as calculi from the RCC family, the intersection calculi, Allen’s interval algebra, cardinal direction calculi, and calculi from the OPRA family. New calculi can be added to the system by specifications in a simple text format or in an XML file format. The tool is designed and implemented with genericity and extensibility in mind, while preserving efficiency and scalability. The user can choose between different data structures and heuristics, and new ones can be easily added to the objectoriented framework. GQR is free software distributed under the terms of the GNU General Public License.
Combining Spatial and Temporal Logics: Expressiveness Vs. Complexity
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2004
"... In this paper, we construct and investigate a hierarchy of spatiotemporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic the spatial logics RCC8, BRCC8, S4 u and their fragments. The obtained results give ..."
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Cited by 25 (9 self)
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In this paper, we construct and investigate a hierarchy of spatiotemporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic the spatial logics RCC8, BRCC8, S4 u and their fragments. The obtained results give a clear picture of the tradeoff between expressiveness and `computational realisability' within the hierarchy. We demonstrate how di#erent combining principles as well as spatial and temporal primitives can produce NP, PSPACE, EXPSPACE, 2EXPSPACEcomplete, and even undecidable spatiotemporal logics out of components that are at most NP or PSPACEcomplete.
A relative orientation algebra with adjustable granularity
 IN: PROCEEDINGS OF THE WORKSHOP ON AGENTS IN REALTIME AND DYNAMIC ENVIRONMENTS (IJCAI
, 2005
"... The granularity of spatial calculi and the resulting mathematical properties have always been a major question in solving spatial tasks qualitatively. In this paper we present the Oriented Point Relation Algebra (OPRAm), a new orientation calculus with adjustable granularity. Since our calculus is a ..."
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Cited by 22 (3 self)
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The granularity of spatial calculi and the resulting mathematical properties have always been a major question in solving spatial tasks qualitatively. In this paper we present the Oriented Point Relation Algebra (OPRAm), a new orientation calculus with adjustable granularity. Since our calculus is a relation algebra in the sense of Tarski, fast standard inference methods can be applied. One of the major problems—depending on the environment, the robots ’ capabilities and the tasks to be solved—is the choice of the granularity of an applied calculus. To present, granularity had to be chosen at the start and could not be changed on the fly. In a dynamically changing environment under real time conditions it is necessary to choose a coarse but still adequate granularity of the spatial representation: only in that case irrelevant feature changes fail to trigger unnecessary inference steps. A qualitative, coarse abstraction suppresses tiny changes in the environment and leads to fast computation.