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Projections in Venn-Euler diagrams

J. Gil, J. Howse, S. Kent, J. Taylor
Proceeding 2000 IEEE International Symposium on Visual Languages  
Venn diagrams and Euler circles have long been used to express constraints on sets and their relationships with other sets.  ...  In order to reduce this clutter, and to focus attention within the diagram appropriately, the notion of a projected contour, or projection, is introduced.  ...  Semantics of Venn-Euler Diagrams In this section we sketch the main definitions used in giving semantics to an Venn-Euler diagram.  ... 
doi:10.1109/vl.2000.874375 dblp:conf/vl/GilHKT00 fatcat:ehe6vbmvjbfxhlr7bc5s67zhju

A Survey of Reasoning Systems Based on Euler Diagrams

Gem Stapleton
2005 Electronical Notes in Theoretical Computer Science  
Euler diagrams have been used for centuries as a means for conveying ideas in an intuitive, informal way.  ...  Most of these systems extend Euler diagrams by adding further syntax to increase expressiveness. In this paper we survey such systems and draw comparisons between them.  ...  The Venn diagram in figure 3 expresses the same information as the Euler diagram in figure 1.  ... 
doi:10.1016/j.entcs.2005.02.022 fatcat:mnf4zv54hvchpkranod5stucdq

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R

Hanbo Chen, Paul C Boutros
2011 BMC Bioinformatics  
Conclusions: The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.  ...  Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment.  ...  Kenneth Chu and Daryl Waggott for help in generating the windowscompatible version of this package.  ... 
doi:10.1186/1471-2105-12-35 pmid:21269502 pmcid:PMC3041657 fatcat:q3lxiqagyrfzphfrbkf67n2b2i

Towards a General Solution to Drawing Area-Proportional Euler Diagrams

Stirling Chow, Frank Ruskey
2005 Electronical Notes in Theoretical Computer Science  
We present a deterministic algorithm for drawing Euler diagrams using n simple polygons so that the regions have a prescribed area.  ...  . , n}, the algorithm can still be applied, but will sometimes create an Euler diagram where the curves are self-intersecting.  ...  For example, to produce a projection of the Euler diagram in Figure 3 , we simply ignore the curves' colors.  ... 
doi:10.1016/j.entcs.2005.02.017 fatcat:phvrnqrddzg4tatxk6cmotma5y

Using DAG Transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Inference

Nik Swoboda, Gerard Allwein
2003 Electronical Notes in Theoretical Computer Science  
It has been shown that a special collection of directed acyclic graphs (DAGs) can be used interchangeably with Euler/Venn diagrams in reasoning processes [4] .  ...  Thus, proofs which include Euler/Venn diagrams can be thought of as proofs with DAGs where steps involving only Euler/Venn diagrams can be treated as particular DAG transformations.  ...  This project began with the description of a technique for using DAGs to represent Euler/Venn diagrams [4] .  ... 
doi:10.1016/s1571-0661(04)80613-3 fatcat:kemfxhsyfvgppbbesvfpwchdwe

Introduction: Varieties of Iconicity

Valeria Giardino, Gabriel Greenberg
2014 Review of Philosophy and Psychology  
In Section 2 we illustrate these ideas with a case study of diagrammatic representation: the evolution from Euler diagrams to Venn diagrams.  ...  We begin in Section 1 with background: the distinction between pictures and diagrams, the concept of systems of representation, and that of the properties of usage associated with signs.  ...  Similarly, a viewer who can interpret one Venn diagram is in a position to interpret any other Venn diagram (but not any other Euler diagram or graph).  ... 
doi:10.1007/s13164-014-0210-7 fatcat:jo2shkuzu5hclhapx6lcr7fisu

Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference

Nik Swoboda, Gerard Allwein
2004 Journal of Software and Systems Modeling  
In previous work, it has been shown that a special collection of directed acyclic graphs (DAGs) can be used interchangeably with Euler/Venn diagrams in reasoning processes.  ...  Thus, proofs which include Euler/Venn diagrams can be thought of as proofs with DAGs where steps involving only Euler/Venn diagrams can be treated as particular DAG transformations.  ...  Acknowledgements The research reported here was supported in part by a contract with the Telecommunications Advancement Organization of Japan entitled, "A study of innovational interaction media for the  ... 
doi:10.1007/s10270-003-0044-8 fatcat:x6bx5hlll5fshjqv4dmdsboeee

Equivalences in Euler-based diagram systems through normal forms

Andrew Fish, John Taylor
2014 LMS Journal of Computation and Mathematics  
In particular, we consider Euler diagrams with shading, and then we conservatively extend the system to include projections, which allow for a much greater degree of flexibility of representation.  ...  properties in the extended system with projections.  ...  The authors would like to acknowledge UK EPSRC grants EP/E011160: Visualisation with Euler Diagrams, and EP/J010898/1: Automatic Diagram Generation. Acknowledgements.  ... 
doi:10.1112/s1461157014000114 fatcat:4clnrsowrjhkzf3kkj65whw2xe

Exact and Approximate Area-Proportional Circular Venn and Euler Diagrams

L. Wilkinson
2012 IEEE Transactions on Visualization and Computer Graphics  
Most existing computer programs that implement Venn and Euler diagrams are limited to three sets.  ...  Scientists conducting microarray and other experiments use Venn and Euler diagrams to analyze and illustrate their results.  ...  ACKNOWLEDGMENTS Simon Urbanek (AT&T Labs) installed the Java code in CRAN. Funding was provided by NSF/DHS grant DMS-FODAVA-0808860  ... 
doi:10.1109/tvcg.2011.56 pmid:21383412 fatcat:jjlztzgddvfmjjruyqih7dj34e

SpEuler: Semantics-preserving Euler Diagrams [article]

Rebecca Kehlbeck, Jochen Görtler, Yunhai Wang, Oliver Deussen
2021 arXiv   pre-print
In the next step, the graph is transformed into a circular layout that maintains the semantics and yields simple Euler diagrams with smooth curves.  ...  Our method conforms to established form guidelines for Euler diagrams regarding semantics, aesthetics, and readability.  ...  ACKNOWLEDGMENTS This work was supported by the German Research Foundation (DFG) within project KE 740/17-2 of the FOR2111 "Questions at the Interfaces" as well as Project-ID 251654672 -TRR 161 "Quantitative  ... 
arXiv:2108.03529v1 fatcat:nlze6ce4srce3dxse7g623mjn4

Heterogeneous Reasoning with Euler/Venn Diagrams Containing Named Constants and FOL

Nik Swoboda, Gerard Allwein
2005 Electronical Notes in Theoretical Computer Science  
In defining this rule we will attempt to capture the "explicit" information content of an Euler/Venn diagram in a way similar to the Observe rule in the Hyperproof [1] system.  ...  The main goal of this paper is to present the basis for a heterogeneous Euler/Venn diagram and First Order Logic (FOL) reasoning system.  ...  For the purposes of this project, free variables and constants in an Euler/Venn diagram will be treated almost identically.  ... 
doi:10.1016/j.entcs.2005.02.023 fatcat:2hhc6yricbfzdnvqca4ed3zie4

Intervene: a tool for intersection and visualization of multiple gene or genomic region sets

Aziz Khan, Anthony Mathelier
2017 BMC Bioinformatics  
Intervene contains three modules: venn to generate Venn diagrams of up to six sets, upset to generate UpSet plots of multiple sets, and pairwise to compute and visualize intersections of multiple sets  ...  Acknowledgements We thank the developers of the tools we have used to build Intervene and Intervene ShinyApp for sharing their code in open-source software.  ...  There are several web-based applications and R packages available to visualize intersections of up-to six list sets in classical Venn, Euler, or Edward's diagrams [11] [12] [13] [14] [15] [16] .  ... 
doi:10.1186/s12859-017-1708-7 pmid:28569135 pmcid:PMC5452382 fatcat:4imbwef3knh5xjdi4hfogpkhra

Formalizing spider diagrams

J. Gil, J. Howse, S. Kent
1999 Proceedings 1999 IEEE Symposium on Visual Languages  
Geared to complement UML and to the specification of large software systems by non-mathematicians, spider diagrams are a visual language that generalizes the popular and intuitive Venn diagrams and Euler  ...  In this extended abstract we describe spider diagrams from a mathematical standpoint and show how their formal semantics in terms of logical expressions can be made.  ...  We have begun to explore rules for reasoning directly with the diagrams, building on recent work in reasoning with Venn diagrams and Euler circles.  ... 
doi:10.1109/vl.1999.795884 dblp:conf/vl/GilHK99 fatcat:lk5g7ooto5etnmvdcpuf3d4kvq

The Advent of Formal Diagrammatic Reasoning Systems [chapter]

Frithjof Dau
2009 Lecture Notes in Computer Science  
This paper discusses the evolution of formal diagrammatic logics, focusing on those systems which are based on Euler and Venn-Peirce diagrams, and Peirces existential graphs.  ...  Recently, this perception was overturned in the mid 1990s, first with seminal work by Shin on an extended version of Venn diagrams.  ...  Acknowledgment The author wants to thank Gem Stapleton from the Visual Modelling Group for her valuable help and provision of diagrams.  ... 
doi:10.1007/978-3-642-01815-2_3 fatcat:qml7w6xy6ncv7fp7n4v4brlo2y

Measuring and Reducing Clutter in Euler Diagrams

Chris John
2005 Electronical Notes in Theoretical Computer Science  
Projections are a notation that bring syntactic efficiency to Euler diagrams and the flexibility to represent relationships between sets in a variety of semantically equivalent ways.  ...  This paper briefly outlines the first sound and complete system of Euler diagrams to incorporate the notation of projections.  ...  Sun-Joo Shin developed several systems based on Venn diagrams [5] and several systems of 'spider diagrams' [6] , [7] , [8] based on Venn and Euler diagrams, have been developed at the University  ... 
doi:10.1016/j.entcs.2005.01.035 fatcat:cdr2olpzlrgxnnokuznyoup7pa
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