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A Theory of Granular Partitions
, 2001
"... This paper presents an application of the theory of granular partitions proposed in (Smith and Brogaard, to appear), (Smith and Bittner 2001) to the phenomenon of vagueness. We understand vagueness as a semantic property of names and predicates. This is in contrast to those views which hold that the ..."
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Cited by 85 (38 self)
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This paper presents an application of the theory of granular partitions proposed in (Smith and Brogaard, to appear), (Smith and Bittner 2001) to the phenomenon of vagueness. We understand vagueness as a semantic property of names and predicates. This is in contrast to those views which hold that there are intrinsically vague objects or attributes in reality and thus conceive vagueness in a de re fashion. All entities are crisp, on de dicto view here defended, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We show that the theory of granular partitions provides a general framework within which we can understand the relation between terms and concepts on the one hand and their multiple referents or extensions on the other, and we show how it might be possible to formulate within this framework a solution to the Sorites paradox. 1.
Spatio-Temporal Predicates
- IEEE Transactions on Knowledge and Data Engineering
, 1999
"... AbstractÐThis paper investigates temporal changes of topological relationships and thereby integrates two important research areas: First, two-dimensional topological relationships that have been investigated quite intensively and, second, the change of spatial information over time. We investigate ..."
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Cited by 57 (15 self)
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AbstractÐThis paper investigates temporal changes of topological relationships and thereby integrates two important research areas: First, two-dimensional topological relationships that have been investigated quite intensively and, second, the change of spatial information over time. We investigate spatio-temporal predicates, which describe developments of well-known spatial topological relationships. A framework is developed in which spatio-temporal predicates can be obtained by temporal aggregation of elementary spatial predicates and sequential composition. We compare our framework with two other possible approaches: one is based on the observation that spatio-temporal objects correspond to three-dimensional spatial objects for which existing topological predicates can be exploited. The other approach is to consider possible transitions between spatial configurations. These considerations help to identify a canonical set of spatio-temporal predicates. Index TermsÐTime in geographic information, spatio-temporal data types, representation of spatio-temporal objects, changes of spatial predicates, developments of spatial objects. 1
Qualitative Extents for Spatio-Temporal Granularity
- Spatial Cognition and Computation
"... The concepts of everywhere and somewhere generate three spatial extents: (1) everywhere, (2) somewhere but not everywhere, and (3) nowhere. These three extents can be used for the granular description of spatial regions. When spatio-temporal regions are considered there are two additional concep ..."
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Cited by 3 (0 self)
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The concepts of everywhere and somewhere generate three spatial extents: (1) everywhere, (2) somewhere but not everywhere, and (3) nowhere. These three extents can be used for the granular description of spatial regions. When spatio-temporal regions are considered there are two additional concepts: always and sometimes. The interaction of the four concepts can be used to produce various systems of spatio-temporal extents. The paper shows that if we want to give granular descriptions of spatio-temporal regions, then the system of extents needs to be chosen carefully. A suitable system of eleven spatio-temporal extents is identi- ed, and a simplied system of six extents is also described. The systems of extents presented here are important in that they will allow various structures and theories understood only in a purely spatial context to be generalized to the spatio-temporal case. Keywords: Granularity, Change, Spatio-Temporal Regions, Formal Theories, Relations between Regions Statement: Neither this paper nor a close simile has been submitted for publication elsewhere. 1
Tutorial ”spatial data types: Conceptual foundation for the design and implementation of spatial database systems and gis
- In The 6th International Symposium on Advances in Spatial Databases
, 1999
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An Extended Partition Model for Generalized Multidimensional Data
, 2007
"... Multidimensional databases have been playing a significant role in the database field. However, some cases may need a more flexible model than the rigid structure of a data cube where all cells in each dimension resolultion combination must be filled. Generally, a data cube may be viewed as a multip ..."
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Multidimensional databases have been playing a significant role in the database field. However, some cases may need a more flexible model than the rigid structure of a data cube where all cells in each dimension resolultion combination must be filled. Generally, a data cube may be viewed as a multiple partition over a population. We propose a two-level formalism for modeling multiple partitions and aggregate data assigned to their component sets, based on partition semantics of attributes. On the lower level, partition relations augmented with cumulative attributes represent the partition data. The user level uses a structural graph of attributes based on functional constraints for describing the schema of the database and for expressing query operations in an attribute-oriented way. The model is flexible to deal with cases like sparse or nested data cubes or with complex relationships or hierarchies among partitioning attributes. 1
Copyright © Springer-Verlag 4 Spatio-temporal Models and Languages:
"... In this chapter we develop DBMSdata models and query languages to deal with geometries changing over time. In contrast to most of the earlier work on this subject, these models and languages are capable of handling continuously changing geometries, or moving objects. We focus on two basic abstractio ..."
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In this chapter we develop DBMSdata models and query languages to deal with geometries changing over time. In contrast to most of the earlier work on this subject, these models and languages are capable of handling continuously changing geometries, or moving objects. We focus on two basic abstractions called moving
CHAPTER 1 A Theory of Granular Partitions
"... Imagine that you are standing on a bridge above a highway checking off the makes and ..."
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Imagine that you are standing on a bridge above a highway checking off the makes and
CHAPTER 7 A Theory of Granular Partitions
"... Imagine that you are standing on a bridge above a highway checking off the makes and models of the cars that are passing underneath. Or that you are a postal clerk dividing envelopes into bundles; or a laboratory technician sorting samples of bacteria into species and subspecies. Or imagine that you ..."
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Imagine that you are standing on a bridge above a highway checking off the makes and models of the cars that are passing underneath. Or that you are a postal clerk dividing envelopes into bundles; or a laboratory technician sorting samples of bacteria into species and subspecies. Or imagine that you are making a list of the fossils in your museum, or of
Representing Topological Relationships for Moving Objects
"... Abstract. Several representations have been created to store topological infor-mation in normal spatial databases. However, not that much work has been done to store such relationships for spatiotemporal data. This paper extends the representation of moving objects from [7] so that it can also store ..."
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Abstract. Several representations have been created to store topological infor-mation in normal spatial databases. However, not that much work has been done to store such relationships for spatiotemporal data. This paper extends the representation of moving objects from [7] so that it can also store and enforce some of the topological relationships between the objects. This is done in a fashion similar to the Node-Arc-Area model for normal spatial databases. One use of such a representation is storing a changing spatial partition. 1
