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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 NP-hard 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 141 (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 NP-hard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC-8. We extend Bennett's encoding of RCC-8 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 RCC-8 that contains all base relations. Further, we show that for this subset path-consistency 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 so-called 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 67 (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
Spatial Reasoning with Topological Information
- Ph.D. thesis, Institut fur Informatik, Albert-Ludwigs-Universitat Freiburg
, 1998
"... . This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the re ..."
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Cited by 60 (2 self)
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. This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the required dimension of the applied space. Further, it includes computational issues, e.g., how hard is it to reason with the calculus and are there efficient algorithms. Finally, we also address cognitive issues, i.e., is the calculus cognitively adequate. 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. Different aspects of space can be treated in a qualitative way. Among others there are approaches considering orientation, distance, shape, topology, and combinations of these. A summary o...
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 RCC-8 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 RCC-8 instances, ..."
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Cited by 52 (12 self)
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The theoretical properties of qualitative spatial reasoning in the RCC-8 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 RCC-8 instances, even if they are in the phase transition region -- provided that one uses the maximal tractable subsets of RCC-8 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.
Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis
- In Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI-99
, 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 47 (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 path-consistency 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,...
Reasoning About Temporal Relations: The Tractable Subalgebras Of Allen's Interval Algebra
- Journal of the ACM
, 2001
"... Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra c ..."
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Cited by 42 (2 self)
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Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NP-complete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.
Temporal Representation and Reasoning in Artificial Intelligence: Issues and Approaches
, 2002
"... this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application ..."
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Cited by 26 (1 self)
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this paper, we survey a wide range of research in temporal representation and reasoning, without committing ourselves to the point of view of any speci c application
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 hard-coded 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 object-oriented framework. GQR is free software distributed under the terms of the GNU General Public License.
Temporal Constraints: A Survey
, 1998
"... . Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints re ..."
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Cited by 26 (1 self)
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. Temporal Constraint Satisfaction is an information technology useful for representing and answering queries about the times of events and the temporal relations between them. Information is represented as a Constraint Satisfaction Problem (CSP) where variables denote event times and constraints represent the possible temporal relations between them. The main tasks are two: (i) deciding consistency, and (ii) answering queries about scenarios that satisfy all constraints. This paper overviews results on several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifying tractable subclasses, (ii) developing exact search algorithms, and (iii) developing polynomial-time approximation algorithms. Most available techniques are based on two principles: (i) enforcing local consistency (e.g. path-consistency), and (ii) enhancing naive backtracking search. Keywords: Temporal Constra...
Twenty-one Large Tractable Subclasses of Allen's Algebra
- ARTIFICIAL INTELLIGENCE
, 1997
"... This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P != NP), in addition to their previously reported ORD-Horn subclass. Furthermore, twelve tractable subclasses are identifi ..."
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Cited by 23 (8 self)
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This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P != NP), in addition to their previously reported ORD-Horn subclass. Furthermore, twelve tractable subclasses are identified, whose maximality is not decided. Four of them can express the notion of sequentiality between intervals, which is not possible in the ORD-Horn algebra. All of the algebras are considerably larger than the ORD-Horn subclass. The satisfiability algorithm, which is common for all the algebras, is shown to be linear. Furthermore, the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras.
