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Probabilistic models for relational data
, 2004
"... We introduce a graphical language for relational data called the probabilistic entityrelationship (PER) model. The model is an extension of the entityrelationship model, a common model for the abstract representation of database structure. We concentrate on the directed version of this model—the di ..."
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Cited by 46 (0 self)
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We introduce a graphical language for relational data called the probabilistic entityrelationship (PER) model. The model is an extension of the entityrelationship model, a common model for the abstract representation of database structure. We concentrate on the directed version of this model—the directed acyclic probabilistic entityrelationship (DAPER) model. The DAPER model is closely related to the plate model and the probabilistic relational model (PRM), existing models for relational data. The DAPER model is more expressive than either existing model, and also helps to demonstrate their similarity. In addition to describing the new language, we discuss important facets of modeling relational data, including the use of restricted relationships, self relationships, and probabilistic relationships. Many examples are provided.
Drawing areaproportional Venn and Euler diagrams
 In Proceedings of Graph Drawing 2003
, 2003
"... Abstract. We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These areaproportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey informatio ..."
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Cited by 46 (1 self)
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Abstract. We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These areaproportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey information about data sets with interacting characteristics. We develop algorithms for drawing areaproportional Venn diagrams for any population distribution over two characteristics using circles and over three characteristics using rectangles and nearrectangular polygons; modifications of these algorithms are then presented for drawing the more general Euler diagrams. We present results concerning which population distributions can be drawn using specific shapes. A program to aid further investigation of areaproportional Venn diagrams is also described. 1
A constraint diagram reasoning system
 Proc. Distributed Multimedia Systems, International Conference on Visual Languages and Computing (VLC '03
, 2003
"... Abstract — The Unified Modeling Language (UML) is a collection of notations which are mainly diagrammatic. These notations are used by software engineers in the process of object oriented modelling. The only textual notation in the UML is the Object Constraint Language (OCL). The OCL is used to expr ..."
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Cited by 29 (19 self)
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Abstract — The Unified Modeling Language (UML) is a collection of notations which are mainly diagrammatic. These notations are used by software engineers in the process of object oriented modelling. The only textual notation in the UML is the Object Constraint Language (OCL). The OCL is used to express logical constraints such as system invariants. Constraint diagrams are designed to provide a diagrammatic alternative to the OCL. Since constraint diagrams are visual they complement existing notations in the UML. Spider diagrams form the basis of constraint diagrams and sound and complete reasoning systems have been developed. Spider diagrams allow subset relations between sets and cardinality constraints on sets to be expressed. In addition to this, constraint diagrams allow universal quantification and relational navigation and hence are vastly more expressive. In this paper we present the first constraint diagram reasoning system. We give syntax and semantics for constraint diagrams we call CD1 diagrams. We identify syntactic criteria that allow us to determine whether a CD1 diagram is satisfiable. We give descriptions of a set of sound and complete reasoning rules for CD1 diagrams. I.
Probabilistic EntityRelationship Models, PRMs, and Plate
, 2007
"... In this chapter, we introduce a graphical language for relational data called the probabilistic entityrelationship (PER) model. The model is an extension of the entityrelationship model, a common model for the abstract representation of database structure. We concentrate on the directed version of ..."
Abstract

Cited by 18 (0 self)
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In this chapter, we introduce a graphical language for relational data called the probabilistic entityrelationship (PER) model. The model is an extension of the entityrelationship model, a common model for the abstract representation of database structure. We concentrate on the directed version of this model—the directed acyclic probabilistic entityrelationship (DAPER) model. The DAPER model is closely related to the plate model and the probabilistic relational model (PRM), existing models for relational data. The DAPER model is more expressive than either existing model, and also helps to demonstrate their similarity. In addition to describing the new language, we discuss important facets of modeling relational data, including the use of restricted relationships, self relationships, and probabilistic relationships. Many examples are provided.
Reasoning with projected contours
 Proc. 2004, LNAI 2980, pp 147–150
, 2004
"... Abstract. Projected contours enable Euler diagrams to scale better. They enable the representation of information using less syntax and can therefore increase visual clarity. Here informal reasoning rules are given that allow the transformation of spider diagrams with respect to projected contours. ..."
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Cited by 10 (0 self)
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Abstract. Projected contours enable Euler diagrams to scale better. They enable the representation of information using less syntax and can therefore increase visual clarity. Here informal reasoning rules are given that allow the transformation of spider diagrams with respect to projected contours. 1 Spider diagrams and projected contours A spider diagram [3] is an Euler diagram with plane trees (spiders) that represent the existence of elements and shading in regions that indicate upper bounds on the cardinalities of sets they denote. Projected contours [1, 2] here are dashed and nonprojected contours are called given contours. The semantics of projected contours are given in [1]: a projected contour represents the intersection of the set denoted by its label with the set denoted by its context (the smallest region, defined in terms of given contours, that it intersects).
Reasoning with Constraint Diagrams
 School of Computing, Mathematical and Information Sciences
, 2004
"... Constraint diagrams are designed for the formal specification of software systems. However, their applications are broader than this since constraint diagrams are a logic that can be used in any formal setting. This document summarizes the main results presented in my PhD thesis, the focus of which ..."
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Cited by 10 (3 self)
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Constraint diagrams are designed for the formal specification of software systems. However, their applications are broader than this since constraint diagrams are a logic that can be used in any formal setting. This document summarizes the main results presented in my PhD thesis, the focus of which is on a fragment of the constraint diagram language, called spider diagrams, and constraint diagrams themselves. In the thesis, sound and complete systems of spider diagrams and constraint diagrams are presented and the expressiveness of the spider diagram language is established. 1
Typesyntax and tokensyntax in diagrammatic systems
 In Proceedings FOIS2001: 2nd International Conference on Formal Ontology in Information Systems
, 2001
"... The uptake in the software industry of notations for designing systems visually has been accelerated with the standardization of the Unified Modeling Language (UML). The formalization of diagrammatic notations is important for the development of essential tool support and to allow reasoning to take ..."
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Cited by 6 (2 self)
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The uptake in the software industry of notations for designing systems visually has been accelerated with the standardization of the Unified Modeling Language (UML). The formalization of diagrammatic notations is important for the development of essential tool support and to allow reasoning to take place at the diagrammatic level. Focusing on an extended version of Venn and Euler diagrams (which was developed to complement UML in the specification of software systems), this paper presents two levels of syntax for this system: typesyntax and tokensyntax. Tokensyntax is about particular diagrams instantiated on some physical medium, and typesyntax provides a formal definition with which a concrete representation of a diagram must comply. While these two levels of syntax are closely related to each other, the domains of typesyntax and tokensyntax are ontologically and the other concrete. We discuss the roles of typesyntax and tokensyntax in diagrammatic systems and show that it is important to consider both levels of syntax in diagrammatic reasoning systems and in developing software tools to support such systems.