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48
On the consistencyof cardinal direction constraints
 Artificial Intelligence
, 2005
"... We present a formal model for qualitative spatial reasoning with cardinal directions utilizing a coordinate system. Then, we study the problem of checking the consistency of a set of cardinal direction constraints. We introduce the first algorithm for this problem, prove its correctness and analyz ..."
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Cited by 15 (2 self)
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We present a formal model for qualitative spatial reasoning with cardinal directions utilizing a coordinate system. Then, we study the problem of checking the consistency of a set of cardinal direction constraints. We introduce the first algorithm for this problem, prove its correctness and analyze its computational complexity. Using the above algorithm, we prove that the consistency checking of a set of basic (i.e., nondisjunctive) cardinal direction constraints can be performed in O(n5) time. We also show that the consistency checking of a set of unrestricted (i.e., disjunctive and nondisjunctive) cardinal direction constraints is NPcomplete. Finally, we briefly discuss an extension to the basic model and outline an algorithm for the consistency checking problem of this extension. 1
Spatial Locations via MorphoMereology
 in Proceedings of KR'2000
, 2000
"... We present a calculus for representing and reasoning about the location of rigid objects which may move within some region (we will speak of mobile parts). The calculus has both a mereological primitive and a morphological one, hence the title of the paper. We present an axiomatisation for con ..."
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Cited by 14 (10 self)
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We present a calculus for representing and reasoning about the location of rigid objects which may move within some region (we will speak of mobile parts). The calculus has both a mereological primitive and a morphological one, hence the title of the paper. We present an axiomatisation for congruence, our chosen morphological primitive, define the notion of mobile part, describe a subset of morphomereological relations suitable for representing spatial locations, and analyze the computational complexity of this set. 1 Introduction Developing formalisms for representing and reasoning about qualitative spatial information is now an active research area, both within AI, and within the field of geographical information systems [14]. Much of the e#ort has been devoted to developing e#cient representations for reasoning about topological information [2, 25, 24, 20], although other aspects such as orientation [22, 19], distance [18] and qualitative morphology [12] have also been ...
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.
Qualitative spatial and temporal reasoning: Efficient algorithms for everyone
 PROCEEDINGS OF THE 20TH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE (IJCAI
, 2007
"... In the past years a lot of research effort has been put into finding tractable subsets of spatial and temporal calculi. It has been shown empirically that large tractable subsets of these calculi not only provide efficient algorithms for reasoning problems that can be expressed with relations contai ..."
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Cited by 12 (4 self)
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In the past years a lot of research effort has been put into finding tractable subsets of spatial and temporal calculi. It has been shown empirically that large tractable subsets of these calculi not only provide efficient algorithms for reasoning problems that can be expressed with relations contained in the tractable subsets, but also surprisingly efficient solutions to the general, NPhard reasoning problems of the full calculi. An important step in this direction was the refinement algorithm which provides a heuristic for proving tractability of given subsets of relations. In this paper we extend the refinement algorithm and present a procedure which identifies large tractable subsets of spatial and temporal calculi automatically without any manual intervention and without the need for additional NPhardness proofs. While we can only guarantee tractability of the resulting sets, our experiments show that for RCC8 and the Interval Algebra, our procedure automatically identifies all maximal tractable subsets. Using our procedure, other researchers and practitioners can automatically develop efficient reasoning algorithms for their spatial or temporal calculi without any theoretical knowledge about how to formally analyse these calculi.
Spatial Logics with Connectedness Predicates
 LOGICAL METHODS IN COMPUTER SCIENCE
, 2010
"... We consider quantifierfree spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected components. We investigate the computational complexity of thes ..."
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Cited by 10 (3 self)
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We consider quantifierfree spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected components. We investigate the computational complexity of these logics and show that the connectedness constraints can increase complexity from NP to PSpace, ExpTime and, if component counting is allowed, to NExpTime.
Combining Topological and Directional Information for Spatial Reasoning ∗
"... Current research on qualitative spatial representation and reasoning usually focuses on one single aspect of space. However, in real world applications, several aspects are often involved together. This paper extends the wellknown RCC8 constraint language to deal with both topological and direction ..."
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Cited by 7 (4 self)
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Current research on qualitative spatial representation and reasoning usually focuses on one single aspect of space. However, in real world applications, several aspects are often involved together. This paper extends the wellknown RCC8 constraint language to deal with both topological and directional information, and then investigates the interaction between the two kinds of information. Given a topological (RCC8) constraint network and a directional constraint network, we ask when the joint network is satisfiable. We show that when the topological network is over one of the three maximal tractable subclasses of RCC8, the problem can be reduced into satisfiability problems in the RCC8 algebra and the rectangle algebra (RA). Therefore, reasoning techniques developed for RCC8 and RA can be used to solve the satisfiability problem of a joint network. 1
Spatial representation and reasoning in RCC8 with Boolean region terms
"... . We extend the expressive power of the region connection calculus RCC8 by allowing to apply the 8 binary relations of RCC8 not only to atomic regions but also to Boolean combinations of them. It is shown that the statisfiability problem for the extended language in arbitrary topological spaces is ..."
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Cited by 5 (0 self)
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. We extend the expressive power of the region connection calculus RCC8 by allowing to apply the 8 binary relations of RCC8 not only to atomic regions but also to Boolean combinations of them. It is shown that the statisfiability problem for the extended language in arbitrary topological spaces is still in NP; however, it becomes PSPACEcomplete if only the Euclidean spaces R n , n ? 0, are regarded as possible interpretations. In particular, in contrast to pure RCC8, the new language is capable of distinguishing between connected and nonconnected topological spaces. 1 INTRODUCTION RCC8 is a logical formalism intended for representing qualitative information about relationships among spatial regions in terms of 8 jointly exhaustive and pairwise disjoint basic binary predicates. It has attracted considerable interest in the spatial reasoning community [1, 2, 8, 12, 14, 15]. Typical expressions of the calcus are: PO(Italy; Alps) (`Italy and the Alps partially overlap'), NTPP(Lux...
Regionbased Theories of Space: Mereotopology and Beyond (PhD Qualifying Exam Report, 2009)
"... The very nature of topology and its close relation to how humans perceive space and time make mereotopology an indispensable part of any comprehensive framework for qualitative spatial and temporal reasoning (QSTR). Within QSTR, it has by far the longest history, dating back to descriptions of pheno ..."
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Cited by 5 (2 self)
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The very nature of topology and its close relation to how humans perceive space and time make mereotopology an indispensable part of any comprehensive framework for qualitative spatial and temporal reasoning (QSTR). Within QSTR, it has by far the longest history, dating back to descriptions of phenomenological processes in nature (Husserl, 1913; Whitehead, 1920, 1929) – what we call today ‘commonsensical ’ in Artificial Intelligence. There have been plenty of other motivations to
Reasoning about cardinal directions between extended objects
 Artif. Intell
"... Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualit ..."
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Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NPComplete problem. For a consistent network of basic CDC constraints, our algorithm also returns a ‘canonical ’ solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n 5). 1