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PaL Diagrams: A Linear Diagram-Based Visual Language

Chapman, Peter, Stapleton, Gem, Rodgers, Peter (2014) PaL Diagrams: A Linear Diagram-Based Visual Language. Journal of Visual Languages and Computing, 25 (6). pp. 945-954. ISSN 1045-926X. (doi:10.1016/j.jvlc.2014.10.022) (KAR id:43500)

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Official URL:
http://dx.doi.org/10.1016/j.jvlc.2014.10.022

Abstract

Linear diagrams have recently been shown to be

more effective than Euler diagrams when used

for set-based reasoning. However, unlike the

growing corpus of knowledge about formal aspects

of Euler and Venn diagrams, there has been no

formalisation of linear diagrams. To fill this

knowledge gap, we present and formalise Point

and Line (PaL) diagrams, an extension of simple

linear diagrams containing points, thus providing

a formal foundation for an effective visual

language.We prove that PaL diagrams are exactly

as expressive as monadic first-order logic with

equality, gaining, as a corollary, an equivalence

with the Euler diagram extension called spider

diagrams. The method of proof provides translations

between PaL diagrams and sentences of monadic

first-order logic.

Item Type: Article
DOI/Identification number: 10.1016/j.jvlc.2014.10.022
Additional information: First version was awarded best paper in VLC 2014. Extended for JVLC Journal
Uncontrolled keywords: Linear Diagrams, Set Visualization
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Peter Rodgers
Date Deposited: 20 Oct 2014 09:36 UTC
Last Modified: 04 Jul 2023 11:24 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/43500 (The current URI for this page, for reference purposes)

University of Kent Author Information

Stapleton, Gem.

Creator's ORCID:
CReDIT Contributor Roles:

Rodgers, Peter.

Creator's ORCID: https://orcid.org/0000-0002-4100-3596
CReDIT Contributor Roles:
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