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Relations defined on sets

by Edmund Woronowicz - Journal of Formalized Mathematics , 1989
"... Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse ima ..."
Abstract - Cited by 510 (0 self) - Add to MetaCart
Summary. The article includes theorems concerning properties of relations defined as a subset of the Cartesian product of two sets (mode Relation of X,Y where X,Y are sets). Some notions, introduced in [4] such as domain, codomain, field of a relation, composition of relations, image and inverse

Defining Virtual Reality: Dimensions Determining Telepresence

by Jonathan Steuer - JOURNAL OF COMMUNICATION , 1992
"... Virtual reality (VR) is typically defined in terms of technological hardware. This paper attempts to cast a new, variable-based definition of virtual reality that can be used to classify virtual reality in relation to other media. The defintion of virtual reality is based on concepts of "presen ..."
Abstract - Cited by 557 (0 self) - Add to MetaCart
Virtual reality (VR) is typically defined in terms of technological hardware. This paper attempts to cast a new, variable-based definition of virtual reality that can be used to classify virtual reality in relation to other media. The defintion of virtual reality is based on concepts of "

Relations and their basic properties

by Edmund Woronowicz - Journal of Formalized Mathematics , 1989
"... Summary. We define here: mode Relation as a set of pairs, the domain, the codomain, and the field of relation; the empty and the identity relations, the composition of relations, the image and the inverse image of a set under a relation. Two predicates, = and ⊆, and three functions, ∪, ∩ and \ are ..."
Abstract - Cited by 1060 (6 self) - Add to MetaCart
Summary. We define here: mode Relation as a set of pairs, the domain, the codomain, and the field of relation; the empty and the identity relations, the composition of relations, the image and the inverse image of a set under a relation. Two predicates, = and ⊆, and three functions

Attitude-Behavior Relations: A Theoretical Analysis and

by Icek Ajzen, Martin Fishbein - Review of Empirical Research, Psychological Bulletin , 1977
"... Research on the relation between attitude and behavior is examined in light of the correspondence between attitudinal and behavioral entities. Such entities are defined by their target, action, context, and time elements. A review of available empirical research supports the contention that strong a ..."
Abstract - Cited by 503 (3 self) - Add to MetaCart
Research on the relation between attitude and behavior is examined in light of the correspondence between attitudinal and behavioral entities. Such entities are defined by their target, action, context, and time elements. A review of available empirical research supports the contention that strong

Relations between the statistics of natural images and the response properties of cortical cells

by David J. Field - J. Opt. Soc. Am. A , 1987
"... The relative efficiency of any particular image-coding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images f ..."
Abstract - Cited by 831 (18 self) - Add to MetaCart
The relative efficiency of any particular image-coding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images

Data cube: A relational aggregation operator generalizing group-by, cross-tab, and sub-totals

by Jim Gray, Adam Bosworth, Andrew Layman, Don Reichart, Hamid Pirahesh , 1996
"... Abstract. Data analysis applications typically aggregate data across many dimensions looking for anomalies or unusual patterns. The SQL aggregate functions and the GROUP BY operator produce zero-dimensional or one-dimensional aggregates. Applications need the N-dimensional generalization of these op ..."
Abstract - Cited by 860 (11 self) - Add to MetaCart
of these operators. This paper defines that operator, called the data cube or simply cube. The cube operator generalizes the histogram, crosstabulation, roll-up, drill-down, and sub-total constructs found in most report writers. The novelty is that cubes are relations. Consequently, the cube operator can be imbedded

Classification in the KL-ONE knowledge representation system

by James G. Schmolze, Thomas A. Lipkis - COGNITIVE SCIENCE , 1985
"... KL-ONE lets one define and use a class of descriptive terms called Concepts, where each Concept denotes a set of objects A subsumption relation between Concepts is defined which is related to set inclusion by way of a semantics for Concepts. This subsumption relation defines a partial order on Conce ..."
Abstract - Cited by 673 (8 self) - Add to MetaCart
KL-ONE lets one define and use a class of descriptive terms called Concepts, where each Concept denotes a set of objects A subsumption relation between Concepts is defined which is related to set inclusion by way of a semantics for Concepts. This subsumption relation defines a partial order

Federated database systems for managing distributed, heterogeneous, and autonomous databases

by Amit P. Sheth, James A. Larson - ACM Computing Surveys , 1990
"... A federated database system (FDBS) is a collection of cooperating database systems that are autonomous and possibly heterogeneous. In this paper, we define a reference architecture for distributed database management systems from system and schema viewpoints and show how various FDBS architectures c ..."
Abstract - Cited by 1218 (34 self) - Add to MetaCart
can be developed. We then define a methodology for developing one of the popular architectures of an FDBS. Finally, we discuss critical issues related to developing and operating an FDBS.

A Behavioral Notion of Subtyping

by Barbara H. Liskov, Jeanette M. Wing - ACM Transactions on Programming Languages and Systems , 1994
"... The use of hierarchy is an important component of object-oriented design. Hierarchy allows the use of type families, in which higher level supertypes capture the behavior that all of their subtypes have in common. For this methodology to be effective, it is necessary to have a clear understanding of ..."
Abstract - Cited by 509 (13 self) - Add to MetaCart
of how subtypes and supertypes are related. This paper takes the position that the relationship should ensure that any property proved about supertype objects also holds for its subtype objects. It presents two ways of defining the subtype relation, each of which meets this criterion, and each of which

Nonmonotonic Reasoning, Preferential Models and Cumulative Logics

by Sarit Kraus, Daniel Lehmann, Menachem Magidor , 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
Abstract - Cited by 626 (14 self) - Add to MetaCart
of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both proof-theoretic and semantic points
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