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A Tractable Subclass of the Block Algebra: Constraint Propagation and Preconvex Relations
, 1999
"... We define, in this paper, for every n 1, ndimensional block algebra as a set of relations, the block relations, together with the fundamental operations of composition, conversion and intersection. We examine the 13 n atomic relations of this algebra which constitute the exhaustive list of t ..."
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Cited by 2 (0 self)
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as the one of preconvexity. We will confine ourselves to the issue of the consistency of block networks which consist of sets of constraints between a finite number of blocks. Showing that the concepts of convexity and preconvexity are preserved by the fundamental operations, we prove the tractability
A New Tractable Subclass of the Rectangle Algebra
 PROCEEDINGS OF THE 16TH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1999
"... This paper presents the 169 permitted relations between two rectangles whose sides are parallel to the axes of some orthogonal basis in a 2dimensional Euclidean space. Elaborating rectangle algebra just like interval algebra, it defines the concept of convexity as well as the ones of weak pre ..."
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Cited by 17 (1 self)
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This paper presents the 169 permitted relations between two rectangles whose sides are parallel to the axes of some orthogonal basis in a 2dimensional Euclidean space. Elaborating rectangle algebra just like interval algebra, it defines the concept of convexity as well as the ones of weak
Reasoning about generalized intervals: Horn representability and tractability
, 2000
"... This paper organizes the topologic forms of the possible relations between generalized intervals. Working out generalized interval algebra on the pattern of point algebra and interval algebra, it introduces the concept of Horn representability just as the one of convexity. It gives the class of H ..."
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of Horn representable relations a simple characterization based on the concept of strong preconvexity. Adapting the propagation techniques designed to solve the networks of constraints between points or between intervals, it shows that the issue of consistency of a Horn representable generalized
Spatial Reasoning about Points in a Multidimensional Setting
"... This paper organizes, for every n 1, the topologic forms of the possible relations between the Cartesian coordinates of two points of the Euclidean space of dimension n over the field of real numbers. Working out n dimensional point algebra on the pattern of point algebra and cardinal relati ..."
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relation algebra, it introduces the concept of convexity just as the one of preconvexity. Adapting the propagation techniques designed to solve point networks or cardinal relation networks, it shows that these concepts are preserved by the fundamental operations of composition, conversion
Spatial Reasoning with Rectangular Cardinal Direction Relations 1
"... Abstract. It is widely accepted that spatial reasoning plays a central role in various artificial intelligence applications. In this paper we study a recent, quite expressive model presented by Skiadopoulos and Koubarakis in [28, 29] for qualitative spatial reasoning with cardinal direction relation ..."
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relations. We consider some interesting open problems of this formalism, mainly concerning finding tractable, expressive enough, subclasses of the full set (i.e., including disjunction) of relations. So far, no such subclass have been found except that of basic relations only. We focus on a small subset
Expressive Power and Complexity in Algebraic Logic
 Journal of Logic and Computation
, 1997
"... Two complexity problems in algebraic logic are surveyed: the satisfaction problem and the network satisfaction problem. Various complexity results are collected here and some new ones are derived. Many examples are given. The network satisfaction problem for most cylindric algebras of dimension four ..."
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Cited by 22 (2 self)
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four or more is shown to be intractable. Complexity is tiedin with the expressivity of a relation algebra. Expressivity and complexity are analysed in the context of homogeneous representations. The modeltheoretic notion of interpretation is used to generalise known complexity results to a range
Qualitative constraints representation for the time and space in SAT
"... In this paper we consider the consistency problem of temporal or spatial qualitive constraint networks. A new encoding making it possible to represent and solve this problem in the framework of the propositional logic is proposed. The denition of this encoding presupposes the existence of a partic ..."
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In this paper we consider the consistency problem of temporal or spatial qualitive constraint networks. A new encoding making it possible to represent and solve this problem in the framework of the propositional logic is proposed. The denition of this encoding presupposes the existence of a
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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. Related fields of research, such as geographic information science
Deciding consistency of a pointduration network with metric constraints
 in TIME’03
, 2003
"... We introduce a new model, MPDN, for quantitative temporal reasoning with points and durations, that supposes an extension of the TCSP formalism and previous pointduration network models. The problem of deciding consistency for a MPDN is shown to be NPcomplete. So, we identify a tractable fragment, ..."
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We introduce a new model, MPDN, for quantitative temporal reasoning with points and durations, that supposes an extension of the TCSP formalism and previous pointduration network models. The problem of deciding consistency for a MPDN is shown to be NPcomplete. So, we identify a tractable fragment
Knowledge Representation fc Reasoning Unit,
"... We present a new framework for reasoning about points, intervals and dura t ionsPoin t Interval Dura t i on Network ( P I D N). The P I D N adequately handles bo th qual i ta t ive and quant i ta ive tempora l in fo rmat ion. We show that I nterval Algebra, Point Algebra, TCSP, P D N and A P D N ..."
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N become special cases of P I D N. The under ly ing algebraic structure of P I D N is closed under composi t ion and intersection. Determ i n i g consistency of P I D N is N P l l a r d. However, we identify some tractable subclasses of P I D N. We show tha t path consistency is not sufficient
Results 1  10
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29