A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
Equivalences in Euler-based diagram systems through normal forms
2014
LMS Journal of Computation and Mathematics
Preserved Fulltext
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. ...
AbstractThe form of information presented can influence its utility for the conveying of knowledge by affecting an interpreter's ability to reason with the information. ...
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
Completeness Proofs for Diagrammatic Logics
[chapter]
2012
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Completeness has been established for such logics, including Euler diagrams, spider diagrams and a fragment of the constraint diagram logic. ...
Visual logics based on Euler diagrams have recently been developed, including generalized constraint diagrams and concept diagrams. ...
NF for Normal Form). ...
doi:10.1007/978-3-642-31223-6_38
fatcat:lceeuz3bifc4jl4k47lsk2bndi
Visualizing Sets: An Empirical Comparison of Diagram Types
[chapter]
2014
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
To address this knowledge gap, this paper empirically evaluates four diagram types: Venn diagrams, Euler diagrams with shading, Euler diagrams without shading, and the less well-known linear diagrams. ...
There are a range of diagram types that can be used to visualize sets. However, there is a significant lack of insight into which is the most effective visualization. ...
An interesting point is that the Euler diagrams with shading and the Venn diagrams used in the study were all well-formed, whereas those that did not use shading were all non-well-formed (see e.g. ...
doi:10.1007/978-3-662-44043-8_18
fatcat:337omwmgvfdu5derbd6uxnn4mi
A Survey of Reasoning Systems Based on Euler Diagrams
2005
Electronical Notes in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Euler diagrams have been used for centuries as a means for conveying ideas in an intuitive, informal way. ...
Recently much research has been conducted to develop formal, diagrammatic reasoning systems based on Euler diagrams. ...
of these diagrams to represent disjunctive information, like a type of disjunctive normal form. ...
doi:10.1016/j.entcs.2005.02.022
fatcat:mnf4zv54hvchpkranod5stucdq
A normal form for spider diagrams of order
2014
Journal of Visual Languages and Computing
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We define a normal form for spider diagrams of order and provide an algorithm, based on the reasoning system, for producing diagrams in our normal form. ...
We develop a reasoning system for an Euler diagram based visual logic, called spider diagrams of order. ...
Our algorithm also contributes to (a) (b) Figure 1 : An Euler and a spider diagram. the recent interest in normal forms for Euler diagram based logics [8] . ...
doi:10.1016/j.jvlc.2014.10.029
fatcat:jli7flztpzbdlcd5f4c3dkm2ia
Two Types of Diagrammatic Inference Systems: Natural Deduction Style and Resolution Style
[chapter]
2010
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Since the 1990s, reasoning with Venn and Euler diagrams has been studied from mathematical and logical viewpoints. ...
On the one hand, a diagram construed as a set of regions corresponds to a disjunctive normal form formula and the inference system based on such diagrams corresponds to a resolution calculus. ...
Euler diagrams in the region-based framework, called Euler diagrams with shading, are obtained by considering some shaded regions of Venn diagrams as "missing" regions. ...
doi:10.1007/978-3-642-14600-8_12
fatcat:zumqerembveatdvradsxx6wyjq
Using DAG Transformations to Verify Euler/Venn Homogeneous and Euler/Venn FOL Heterogeneous Rules of Inference
2003
Electronical Notes in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
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. ...
To define observation for all formulas in monadic first order logic (MFOL), we introduce a special normal form called EVCNF. ...
doi:10.1016/s1571-0661(04)80613-3
fatcat:kemfxhsyfvgppbbesvfpwchdwe
Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference
2004
Journal of Software and Systems Modeling
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
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
Intuitionistic Euler-Venn Diagrams (extended)
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We present an intuitionistic interpretation of Euler-Venn diagrams with respect to Heyting algebras. ...
In contrast to classical Euler-Venn diagrams, we treat shaded and missing zones differently, to have diagrammatic representations of conjunction, disjunction and intuitionistic implication. ...
For an Euler-Venn diagram d = (L, Z, Z * ) we will write Venn(d) = (L, Venn(L), Z * ) for the Venn diagram with the same set of shaded zones as d, and Euler(d) = (L, Z) for the pure Euler diagram with ...
arXiv:2002.02929v1
fatcat:oiin6blqajhxhlaq6vfhrmpimu
Tactical Diagrammatic Reasoning
2017
Electronic Proceedings in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In this paper we take an interactive proof assistant for Euler diagrams, Speedith, and add tactics to its reasoning engine, providing a level of automation in the construction of proofs. ...
Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. ...
Although our work is concerned only with Euler diagrams, we chose Speedith as the basis for extension due to its code base with effective visualisation of all Euler diagrams. ...
doi:10.4204/eptcs.239.3
fatcat:nvd7gb3ti5ag3p32zy5t22iv3i
On the Completeness and Expressiveness of Spider Diagram Systems
[chapter]
2000
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2004; you can also visit the original URL.
The file type is application/pdf.
Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. ...
A set of reasoning rules for a spider diagram system is shown to be sound and complete. ...
Our longer term aim is to prove similar results for constraint diagrams, and to provide the necessary mathematical underpinning for the development of software tools to aid the diagrammatic reasoning process ...
doi:10.1007/3-540-44590-0_8
fatcat:4wji7m6flfggzdl75nu7aebm5i
Proof-Theoretical Investigation of Venn Diagrams: A Logic Translation and Free Rides
[chapter]
2012
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Then we study a logic translation of the Venn diagrammatic system with the aim of investigating how our inference rules are rendered to resolution calculus. ...
Furthermore, our translation provides a more in-depth analysis of the free ride. In particular, we calculate how many pieces of information are obtained in the manipulation of Venn diagrams. ...
For any non-empty clause set Γ = {r 1 , . . . , r m }, we denote by d(Γ), the disjunctive normal form (DNF) formula (∧r 1 ) ∨ · · · ∨ (∧r m ). ...
doi:10.1007/978-3-642-31223-6_17
fatcat:jflfezsj4zgyrhxz3enxai7fx4
Fragments of Spider Diagrams of Order and Their Relative Expressiveness
[chapter]
2010
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Investigating the expressiveness of a diagrammatic logic provides insight into how its syntactic elements interact at the semantic level. Moreover, it allows for comparisons with other notations. ...
The techniques employed by Shin for Venn-II were adapted to allow the expressiveness of Euler diagrams to be investigated. ...
Acknowledgements This research forms part of the the Defining Regular Languages with Diagrams (EPSRC grant EP/H012311/1) and Sketching Euler Diagrams (EPSRC grant EP/H048480/1) projects. ...
doi:10.1007/978-3-642-14600-8_10
fatcat:6h3jelafjncvbcrftt3e44xgc4
Heterogeneous Reasoning with Euler/Venn Diagrams Containing Named Constants and FOL
2005
Electronical Notes in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
The main goal of this paper is to present the basis for a heterogeneous Euler/Venn diagram and First Order Logic (FOL) reasoning system. ...
We will begin by defining a homogeneous reasoning system for Euler/Venn diagrams including named constants and show this system to be sound and complete. ...
This is done to ensure that any Euler/Venn diagram with shading can be redrawn as a logically equivalent Euler/Venn diagram with any shaded area removed. ...
doi:10.1016/j.entcs.2005.02.023
fatcat:2hhc6yricbfzdnvqca4ed3zie4
Drawing Graphs in Euler Diagrams
[chapter]
2004
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
However, we show our system being used with a form of constraint diagram, the spider diagram [9] . ...
The shaded zone in the drawn diagram corresponds to the abstract zone {a}. ...
We would also like to thank John Taylor and Richard Bosworth at the University of Brighton for helpful comments on early versions of this paper. ...
doi:10.1007/978-3-540-25931-2_9
fatcat:35rucpfugnhl7fdkicjekn6b4q
« Previous
Showing results 1 — 15 out of 7,494 results