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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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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
Spatial and temporal reasoning: beyond Allen's calculus
 AI Communications
"... Temporal knowledge representation and reasoning with qualitative temporal knowledge has now been around for several decades, as formalisms such as Allen’s calculus testify. Now a variety of qualitative calculi, both temporal and spatial, has been developed along similar lines to Allen’s calculus. T ..."
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Cited by 8 (1 self)
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Temporal knowledge representation and reasoning with qualitative temporal knowledge has now been around for several decades, as formalisms such as Allen’s calculus testify. Now a variety of qualitative calculi, both temporal and spatial, has been developed along similar lines to Allen’s calculus. The main object of this paper is to point to open questions which arise when, leaving the now wellchartered waters of Allen’s, we venture into rougher sea of these formalisms. What remains true among the properties of Allen’s calculus? Partial answers are indeed known, but numerous new problems also arise. We try to point to the main issues in this paper.
, Knowledge Representation and Reasoning Group
"... Abstract. What is a qualitative calculus? Many qualitative spatial and temporal calculi arise from a set of JEPD (jointly exhaustive and pairwise disjoint) relations: a stock example is Allen’s calculus, which is based on thirteen basic relations between intervals on the time line. This paper examin ..."
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Abstract. What is a qualitative calculus? Many qualitative spatial and temporal calculi arise from a set of JEPD (jointly exhaustive and pairwise disjoint) relations: a stock example is Allen’s calculus, which is based on thirteen basic relations between intervals on the time line. This paper examines the construction of such a formalism from a general point of view, in order to make apparent the formal algebraic properties of all formalisms of that type. We show that the natural algebraic object governing this kind of calculus is a nonassociative algebra (in the sense of Maddux), and that the notion of weak representation is the right notion for describing most basic properties. We discuss the ubiquity of weak representations in various guises, and argue that the fundamental notion of consistency itself can best be understood in terms of consistency of one weak representation with respect to another. 1
New Ways to Handle Spatial Relations through Angle plus MBR Theory on Raster Documents
, 2009
"... The paper presents novel ideas on spatial reasoning by considering shape and size of spatial entities and focuses on extension of conventional models: ConeShaped and Minimum Boundary Rectangle (MBR). Firstly, it goes on the use of how well MBR features fixed to coneshaped model considering the rel ..."
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The paper presents novel ideas on spatial reasoning by considering shape and size of spatial entities and focuses on extension of conventional models: ConeShaped and Minimum Boundary Rectangle (MBR). Firstly, it goes on the use of how well MBR features fixed to coneshaped model considering the relative extension of the spatial entities. This suggests the further possibility and the quality of combinatorial study of the models in spatial reasoning. Secondly, another model is proposed by referencing a unique common point set (of two entities) instead of using one out of two entities (referencing in a conventional way). This makes model robust and more symmetric as it reserves two way relationships from the unique reference point set. Further, it gives flexibility to utilize conventional models. Finally, it gives a comparative idea of proposed models among existing ones.
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, 2014
"... Publication details, including instructions for authors and subscription information: ..."
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