Results 11  20
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51
Map Graphs
, 1999
"... We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, and an O(n³)time ..."
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Cited by 36 (3 self)
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We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, and an O(n³)time recognition algorithm for a restricted version: given a graph, decide whether it is realized by adjacencies in a map without holes, in which at most four nations meet at any point.
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.
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.
On the Computational Complexity of SpatioTemporal Logics
 Proceedings of the 16th AAAI International FLAIRS Conference
, 2003
"... Recently, a hierarchy of spatiotemporal languages based on the propositional temporal logic PTL and the spatial languages RCC8, BRCC8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open. ..."
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Cited by 22 (0 self)
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Recently, a hierarchy of spatiotemporal languages based on the propositional temporal logic PTL and the spatial languages RCC8, BRCC8 and S4u has been introduced. Although a number of results on their computational properties were obtained, the most important questions were left open.
Combining Topological and Qualitative Size Constraints for Spatial Reasoning
, 1998
"... . Information about the relative size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we combine a simple framework for reasoning about qualitative size relations with the Region Connection Cal ..."
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Cited by 21 (4 self)
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. Information about the relative size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we combine a simple framework for reasoning about qualitative size relations with the Region Connection Calculus RCC8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC8 relations is NPhard, but a large maximal tractable subclass of RCC8 called b H8 was identified. Interestingly, any constraint in RCC8 \Gamma b H8 can be consistently reduced to a constraint in b H8 , when an appropriate size constraint between the spatial regions is supplied. We propose an O(n 3 ) time pathconsistency algorithm based on a novel technique for combining RCC8 constraints and relative size constraints, where n is the number of spatial regions. We prove its correctness and completeness for deciding consistency when the input contains topological ...
Combining Topological and Size Information for Spatial Reasoning
 Artificial Intelligence
, 2000
"... Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Regi ..."
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Cited by 21 (8 self)
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Information about the size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we introduce four classes of qualitative and metric size constraints, and we study their integration with the Region Connection Calculus RCC8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC8 relations is NPhard, but three large maximal tractable subclasses of RCC8, called b H8 , C8 and Q8 respectively, have been identied. We propose an O(n 3 ) time pathconsistency algorithm based on a novel technique for combining RCC8 relations and qualitative size relations forming a Point Algebra, where n is the number of spatial regions. This algorithm is correct and complete for deciding consistency when the topological relations are either in b H8 , C8 or Q8 , and has the same complexity as the best known method for deciding consistency...
D.C.: From video to RCC8: exploiting a distance based semantics to stabilise the interpretation of mereotopological relations
 Proc. COSIT, In Press (2011
"... Abstract. Mereotopologies have traditionally been defined in terms of the intersection of point sets representing the regions in question. Whilst these semantic schemes work well for purely topological aspects, they do not give any semantic insight into the degree to which the different mereotopolog ..."
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Cited by 14 (4 self)
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Abstract. Mereotopologies have traditionally been defined in terms of the intersection of point sets representing the regions in question. Whilst these semantic schemes work well for purely topological aspects, they do not give any semantic insight into the degree to which the different mereotopological relations hold. This paper explores this idea of a distance based interpretation for mereotopology. By introducing a distance measure between x and y, and for various Boolean combinations of x and y, we show that all the RCC8 relations can be distinguished. We then introduce a distance measure which combines these individual measures which we show reflect different paths through the RCC8 conceptual neighbourhood – i.e. the measure decreases/increases monotonically given certain monotonic transitions (such as one region expanding). There are several possible applications of this revised semantics; in the second half of the paper we explore one of these in some depth – the problem of abstracting mereotopological relations from noisy video data, such that the sequences of qualitative relations between pairs of objects do not suffer from “jitter”. We show how a Hidden Markov Model can exploit this distance based semantics to yield improved interpretation of video data at a qualitative level. 1
Spatial reasoning in a fuzzy region connection calculus
 Artificial Intelligence
, 2009
"... Although the region connection calculus (RCC) offers an appealing framework for modelling topological relations, its application in real–world scenarios is hampered when spatial phenomena are affected by vagueness. To cope with this, we present a generalization of the RCC based on fuzzy set theory, ..."
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Cited by 13 (2 self)
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Although the region connection calculus (RCC) offers an appealing framework for modelling topological relations, its application in real–world scenarios is hampered when spatial phenomena are affected by vagueness. To cope with this, we present a generalization of the RCC based on fuzzy set theory, and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems. We furthermore reveal that reasoning in our fuzzy RCC is NP–complete, thus preserving the computational complexity of reasoning in the RCC, and we identify an important tractable subfragment. Moreover, we show how reasoning tasks in our fuzzy RCC can also be reduced to reasoning tasks in the original RCC. While this link with the RCC could be exploited in practical reasoning algorithms, we mainly focus on the theoretical consequences. In particular, using this link we establish a close relationship with the Egg–Yolk calculus, and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension.
Terminological default reasoning about spatial information: A first step
 In Proc. of COSIT’99, International Conference on Spatial Information Theory
, 1999
"... Abstract. We extend the theory about terminological default reasoning by using a logical base language that can represent spatioterminological phenomena. Based on this description logic language called ALCRP(S2), which is briefly introduced, we discuss algorithms for computing socalled extensions ( ..."
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Cited by 12 (9 self)
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Abstract. We extend the theory about terminological default reasoning by using a logical base language that can represent spatioterminological phenomena. Based on this description logic language called ALCRP(S2), which is briefly introduced, we discuss algorithms for computing socalled extensions (“possible worlds”) of a world description and a set of defaults. We conclude with an application of the theory to problems in visual query systems and demonstrate the significance of the theory for spatioterminological reasoning in general and spatioterminological default reasoning in particular. 1
B.C.: Representing Qualitative Spatial Information in OWLDL
 In: Proceedings of OWL: Experiences and Directions
, 2005
"... The Web Ontology Language has not been designed for representing spatial information, which is often required for applications such as Spatial Databases and Geographical Information Systems. As a consequence, many existing OWL ontologies have little success in encoding spatial information. In this p ..."
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Cited by 11 (0 self)
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The Web Ontology Language has not been designed for representing spatial information, which is often required for applications such as Spatial Databases and Geographical Information Systems. As a consequence, many existing OWL ontologies have little success in encoding spatial information. In this paper, we argue that the representation of spatial information is not a fundamental limitation of OWL. In fact, OWLDL does provide some of the expressive power required for representation of spatial regions and their relationships. However, a direct representation is far from intuitive. In the last decade, several languages for the representation of the relations between spatial regions have been developed. Among these formalisms for qualitative spatial reasoning, the RCC8 fragment of the Region Connection Calculus, which introduces a set of eight basic relationships between regions on the plane, has received special attention. In this paper, we outline a translation of the RCC8 calculus into OWLDL, by adapting some of the known results on the translation of qualitative spatial