Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings (Lecture Notes in Computer Science)

This book constitutes the refereed proceedings of the 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, held virtually in September 2021. The 16 full papers and 25 short papers presented together with 16 posters were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: design of concrete diagrams; theory of diagrams; diagrams and mathematics; diagrams and logic; new representation systems; analysis of diagrams; diagrams and computation; cognitive analysis; diagrams as structural tools; formal diagrams; and understanding thought processes. 10 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. Preface Organization Abstracts of Keynotes A Philosophical View of Fundamental Properties of Diagrams Why and How Should We Draw to Learn Learning from Visual Displays: Processes and Interventions Diagrams and Dicisigns: The Interrelations of Peirce’s Doctrines of Propositions and Diagrammatical Reasoning Contents Design of Concrete Diagrams Aesthetics and Ordering in Stacked Area Charts 1 Introduction 2 Related Work 3 Aesthetic Criteria for Stacked Area Charts 3.1 Flatness: Minimising Wiggle 3.2 Straightness: Minimising Bumps 3.3 Continuity: Minimising Broken Layers 3.4 Significance: Minimising the Influence of Thin Layers 3.5 Choosing One or More Representative Lines 4 Ordering Layers 4.1 Objective Function 4.2 Optimisation Procedure 5 Benchmarking 6 Conclusion References Interactive, Orthogonal Hyperedge Routing in Schematic Diagrams Assisted by Layout Automatisms 1 Introduction 2 Related Work 3 Interactive Routing of Hyperedges 4 Automatic Routing Considering Manual Changes 5 Conclusion References Evidence of Chunking in a Simple Drawing Task 1 Introduction 2 Sample Analysis: Inferring Potential Chunks from Pauses 3 Discussion References Theory of Diagrams Considerations in Representation Selection for Problem Solving: A Review 1 Introduction 2 Cognitive Factors in Problem Solving 2.1 Problem Solving 2.2 Space Traversal and Expertise 2.3 Cognitively Effective Representations 3 Heterogeneity of Representations 3.1 Diagrammatic Aspects of Representations 3.2 Recommending a Representation 4 Computational Considerations of Representation 4.1 Homogeneous Systems 4.2 Semi-heterogeneity 4.3 Fully Heterogeneous Theorem Provers 5 Cognitive Analysis of Computational Systems 6 Conclusion References Diagrams as Part of Physical Theories: A Representational Conception 1 Introduction 2 Conceptions of Scientific Theories 3 Semantic-Representational View on Theories 4 Case Study: Phase Space Diagrams in Statistical Mechanics 5 Conclusion References Diagrams and Mathematics Beyond Counting: Measuring Diagram Intensity in Mathematical Research Papers 1 Introduction 2 Detecting and Measuring Diagrams 3 Measuring Textual Proxies for Diagrams 4 Contemporary Use of Diagrams in Mathematical Research 5 Conclusions and Further Perspectives References On the Relationship Between Geometric Objects and Figures in Euclidean Geometry 1 Introduction 2 Geometric Figures in Practical Geometry 3 Relating Geometric Objects to Geometric Figures 4 Basic Features of the Role of Diagrams in Pure and Applied Geometry 5 Conclusions References What Diagrams Are Considered Useful for Solving Mathematical Word Problems in Japan? 1 Introduction 2 Method 3 Results and Discussion References Diagrams and Logic The Search for Symmetry in Hohfeldian Modalities 1 Introduction 2 Background and Related Works 3 Formalization 3.1 Language 3.2 First-Order Hohfeldian Relations 3.3 Second-Order Hohfeldian Relations 4 Hohfeldian Squares and Aristotelian squares 4.1 Deontic Square of Opposition 4.2 O'Reilly's (or Change-Centered) Potestative Square of Opposition 4.3 Force-Centered Potestative Square of Opposition 4.4 Outcome-Centered Potestative Square of Opposition 5 Of Lost Symmetries 5.1 Half-Liberties and Full-Liberties 5.2 Disjoint or Absolute Duty 6 Prototypical Relations Between the Two Squares 7 Conclusion References Wittgenstein’s Picture-Investigations 1 Introduction 1.1 The Presence of Literal Pictures 1.2 The Function of Images 1.3 Propositions, Non-propositions and Pictures 1.4 Problem Statement and Present Aims 2 Method 2.1 Discussion 3 Case Studies 3.1 Propositions as Pictures and Pictures as Propositions 3.2 Images Within Quotation Marks (Picture-Assertions) 3.3 Images Collocated with “example, thus:, like this:” (Picture-Samples) 3.4 Images Collocated with “Rule” (Picture-Rules) 3.5 Images Collocated with “Proof” (Picture-Proofs as Picture-Acts) 4 Conclusions and Future Research 4.1 Picture-sentences as Propositions 4.2 Picture-sentences as Rules 4.3 Future Research: The Potential for Pictures as Hinges References What Kind of Opposition-Forming Operator is Privation? 1 Introduction 2 TL: The Term Logic of Privation 2.1 Syntax of TL 2.2 Semantics and Consequence 3 Some Textual Evidence for Semantics of Privative Terms 3.1 Two-Term and Tree-Term Propositions 3.2 Correia's Analysis 4 Privation as Opposition-Forming Operator 5 Conclusion References Presenting Basic Graph Logic 1 Introduction 2 Syntax of Basic Graph Logic 3 Semantics of Basic Graph Logic 4 Validity and Consequence in Basic Graph Logic 5 Diagrammatic Proofs in Basic Graph Logic 6 Final Remarks References Schopenhauer's Partition Diagrams and Logical Geometry 1 Introduction 2 Aristotelian Relations and -Structures 3 The Context of Schopenhauer's Partition Diagrams 4 Schopenhauer's Partition Diagrams 5 From Partition Diagrams to -Structures 6 Conclusion References Revisiting Peirce's Rules of Transformation for Euler-Venn Diagrams 1 Introduction 2 Rules 1 to 3 3 Rule 4 4 Rules 5 to 6 5 Comparison with Modern Diagrammatic Systems 6 Conclusion References Tractarian Notations 1 Tractarian Extensionality 2 Propositional Signs 3 Tabular and Operational Notations References Equivalence Proof for Intuitionistic Existential Alpha Graphs 1 Introduction 2 The System of Intuitionistic Alpha Graphs 3 From Formulas to Graphs 4 A System of Strings 5 From Graphs to Formulas 6 Concluding Remarks References Aaron Schuyler: The Missing Link Between Euler and Venn Diagrams? 1 Schuyler’s Role in the Venn-Hamilton Dispute 2 A Shared Mistake: Does the Exclusion Really Have an Unambiguous Representation in the Euler Diagram? 3 No Non-s is Non-p:A Surprising Diagram 4 How to Represent Four Classes Using Only Two Intersecting Circles 5 Conclusions References Validity as Choiceless Unification 1 Introduction 2 Universal Syllogisms as Trios of Total Inclusion 3 Universal Syllogisms as Trios of Total Exclusion 4 Particular Syllogisms 5 Conclusive Remarks References Truth Tables Without Truth Values: On 4.27 and 4.42 of Wittgenstein's Tractatus 1 Introduction 2 The Formulas Explained from a Combinatorial Point of View 3 Tautology and Contradiction 4 Wittgenstein's Truth Tables 5 Truth Tables Without Truth Values References Combining and Relating Aristotelian Diagrams 1 Introduction 2 Relating Diagrams 3 Combining Diagrams 4 Examples 5 Conclusion and Outlook References Residuation in Existential Graphs 1 Introduction 2 Beta Graphs and Relational Operations 3 Residuation in Existential Graphs 4 Two Further Examples of Residuation in EGs 5 Concluding Remarks References On Identity in Peirce’s Beta Graphs 1 Introduction: Peirce’s Beta System for Existential Graphs 2 The Logic of Identity in the Beta System 3 Existential Graphs as an Analytical Tool 4 The Function of the Line of Identity 5 Conclusions 1. References Peirce's Diagrammatic Solutions to `Peirce's Puzzle' 1 Introduction 2 Discussion and Conclusions References What Are Rules for? A Carroll-Peirce Comparison 1 Introduction 2 An Instructive Development 3 What Are Rules for? References A Diagrammatic Representation of Hegel's Science of Logic 1 Introduction 2 Allihn's Antibarbarus Logicus and the Hegel Diagram 3 Interpretation of Allihn's Hegel Diagram 4 Discussion References Jin Yuelin’s Simplification of Venn Diagrams 1 Introduction 2 Venn Diagrams and Existential Graphs 3 Venn Diagrams in Jin Yuelin’s 1935 Book Logic 4 Some Remarks on Dashed Circles in Venn Diagrams 5 Conclusion References Venn Diagrams with “Most”: A Natural Logic Approach 1 Introduction 2 Rescher’s Diagram 3 Two Comments on Rescher’s Rules 4 Arrow for “Most” in Natural Logic 5 Conclusion References New Representation Systems New Representations of Modal Functions 1 Introduction 2 Boolean Operations 2.1 Unary Boolean Operations 2.2 Binary Boolean Operations 3 Modal Operations 3.1 Unary Modal Functions 3.2 Unary Modal Operations on A2 3.3 Modal Functions as Moody Truth-Functions 4 Binary Modal Functions 5 Conclusion References Diagramming Imprecise and Incomplete Temporal Information 1 Introduction 2 Building Blocks 3 Applicability to Temporal Relations 4 Combining Intervals and Points 5 Future Directions References Comics and Diagrams: An Introductory Overview 1 Introduction: The Impossible Definition(s) 1.1 Comics, Maps and Diagrams 1.2 The Grid 2 The Evolutionary Structure 3 Micro-narrations 4 Centripetal Narrations 5 Conclusions References Analysis of Diagrams Image Schemas and Conceptual Blending in Diagrammatic Reasoning: The Case of Hasse Diagrams 1 Introduction 2 Background 3 Approach 3.1 Diagrammatic Syntax and Its Formalisation 3.2 A Formal Model of Sense-Making 4 Related Work 5 Discussion 5.1 Diagrammatic Inference with Image-Schematic Blends 5.2 Efficacy of Diagrammatic Representations 5.3 Conclusions and Future Work A FOL Specifications of Image Schemas and Blends A.1 The Hasse Geometric Configuration A.2 Image Schemas A.3 The Hasse Blend References Through the Eyes of an Archeologist: Studying the Role of Prior Knowledge in Learning with Diagrams 1 Introduction 2 Assumptions in the Study of Learning with Diagrams 2.1 The Directness of Visual Representations 2.2 The Sameness of the Producers and Users of Instructional Materials 3 The Learner as an Archeologist 4 A Formal Framework with Recursive Rules 4.1 Representation as a Three-Place Predicate 4.2 A Set of Test Patterns 4.3 Denotation, the Regular Case of Instructional Material 4.4 Connotation or Figurative Meaning 4.5 Metalanguage 4.6 Mutual Recursion 5 Conclusion References The Fall and Rise of Resemblance Diagrams 1 Entering the Valley of Formalism 2 Methods 3 Results 3.1 Resemblance Diagrams 1885–1895 3.2 Resemblance Diagrams 2005–2015 4 Discussion References The Science of Seeing Science: Examining the Visuality Hypothesis 1 Graph Use in Science 1.1 Disciplinary Differences in Graph and Table Use 1.2 Purpose of the Current Study 2 Method 2.1 Selecting and Coding the Sample 3 Results 3.1 Inscription Use Per Discipline 3.2 Data Presentation and Visuality Indices 4 Discussion 4.1 Implications of Current Study 4.2 Conclusions References Can Humans and Machines Classify Photographs as Depicting Negation? 1 Introduction 2 Experiments 2.1 Negation and Negation-Free Photograph Data Collection 2.2 Machine Learning on the Negation Image Classification Task 2.3 Human Performance on the Negation Image Classification Task 3 Discussion References The Presence of Diagrams and Problems Requiring Diagram Construction: Comparing Mathematical Word Problems in Japanese and Canadian Textbooks 1 Introduction 2 Method 3 Results and Discussion 3.1 Math Word Problems Accompanied by Diagrams in Textbooks 3.2 Types of Diagrams Presented with Math Word Problems 3.3 Problems Requiring the Use of Diagrams References Diagrams and Computation Extracting Interactive Actor-Based Dataflow Models from Legacy C Code 1 Introduction 2 Actor-Based Dataflow Visualization 2.1 Actor-Based Dataflow 2.2 Constructing Actor Models 2.3 Data Types 3 Implementation and Validation 4 Survey 5 Related Work 6 Conclusions and Outlook References Visualising Lattices with Tabular Diagrams 1 Introduction 2 Euler Diagrams and FCA 3 Tabular Diagrams 4 More Examples of Tabular Diagrams 5 Conclusion References Understanding Scholarly Neural Network System Diagrams Through Application of VisDNA 1 Introduction 2 Background 2.1 Neural Network Systems 2.2 Frameworks for Analysing Diagrammatic Representations 3 Application of VisDNA ``Mode of Visual Encoding'' to Scholarly Neural Network Systems Diagrams 3.1 Methodology 3.2 Applying VisDNA 3.3 Example Diagram 4 Results and Discussion 4.1 Strengths of Applying the Framework 4.2 Refinements and Extensions to Improve Utility of VisDNA for (Scholarly NN) System Diagrams 4.3 Limitations 5 Conclusion References A Universal Grammar for Specifying Visualization Types 1 Purpose of This Work 2 A Grammar for ‘Parts of Graphical Speech’ 3 ‘DNA’ and ‘Species’ – A Metaphor for Visualizations 4 Visual Encodings: Arranging, Varying, Linking 5 A Visual Grammar for Combining VisDNA Building Blocks 6 VisDNA Specification Trees 7 Verbal Statements and Visual Statements 8 VisDNA Specification Trees and Linguistic Parse Trees 9 Future Work References Visualizing Program State as a Clustered Graph for Learning Programming 1 Introduction 2 Method 3 Results 4 Conclusion References Dynamic Flowcharts for Enhancing Learners' Understanding of the Control Flow During Programming Learning 1 Introduction and Related Work 2 Method 3 Results 4 Conclusion References Cognitive Analysis Cognitive Properties of Representations: A Framework 1 Introduction 2 Analysis Framework 3 Sample Representations and Problem 4 General Cognitive Property – Sub-RS-Variety 5 Registration Cognitive Properties 6 Semantic Encoding Cognitive Properties 7 Inference Cognitive Properties 8 Problem Solution Cognitive Properties 9 Example of Application 9.1 Evaluation 10 Discussion References Intentional Diagram Design: Using Gestalt Perceptual Grouping in Cladograms to Tackle Misconceptions 1 Introduction 1.1 Understanding Evolutionary Trees 1.2 Conception and Perception 2 Experiment 2.1 Method 2.2 Results 3 Discussion References Cognitive Style’s Effects on User Task Performance in Network Visualisations 1 Introduction 1.1 Current Study 2 Method 2.1 Participants 2.2 Cognitive Style Measures 2.3 Visualisation Efficiency 2.4 Procedure and Visualisation Tasks 3 Results 4 Discussion and Conclusion References Concentrating Competency Profile Data into Cognitive Map of Knowledge Diagnosis 1 Introduction 2 Method 3 Results 4 Conclusion References Diagrams as Structural Tools Interactivity in Linear Diagrams 1 Introduction 2 Interaction Design 2.1 Interactive Elements in Linear Diagrams 3 First Study: Interactive vs. Static Diagrams 3.1 Study Design and Materials 3.2 Hypotheses 3.3 Methods 3.4 Interaction vs. Static Results 3.5 User-Generated Diagrams 4 Second Study: User-Generated vs. Original Diagrams 4.1 Hypotheses 4.2 Results 5 Conclusions and Further Work References Diagrammatic Representations of Uncertainty in Meteorological Forecasting 1 Introduction 2 Philosophy and Meteorology: Some Background 3 Meteorological Prediction in the United States 4 Diagrammatic Representations of Uncertainty in Graphical Weather Products 4.1 The Storm Prediction Center (SPC) 4.2 The National Hurricane Center (NHC) 4.3 The National Weather Service 5 Conclusion 5.1 Practical Orientation of Diagrammatic Representations 5.2 Credibility Maintenance 5.3 The Nature of Uncertainty References Structuralist Analysis for Neural Network System Diagrams 1 Introduction 2 Related Work 2.1 Scientific Diagrams 2.2 Diagrammatic Representations 3 Neural Network Diagram Empirics 3.1 Context 3.2 Method 3.3 Analysis 3.4 Limitations 3.5 Discussion 4 Conclusion References Modeling Multimodal Interactions and Feedback for Embodied Geovisualization 1 Introduction 2 Results References Formal Diagrams On the Cognitive Potential of Derivative Meaning in Aristotelian Diagrams 1 Introduction 2 Abstraction Tracking with Triangular Subdiagrams 2.1 JSB Triangles Versus SC Triangles 2.2 Alternative JSB Versus SC Triangles 3 Abstraction Tracking with Embedded Squares 3.1 Classical Squares Inside JSB Versus SC Hexagons 3.2 Degenerate Squares in Buridan and Béziau octagons 4 Conclusion References Number and Quality of Diagrams in Scholarly Publications is Associated with Number of Citations 1 Introduction 2 Background 3 Method 4 Results 4.1 Diagrams in Context 4.2 Conference Areas 4.3 Neural Network System Diagram Guideline Conformity 5 Related Work 6 Discussion 6.1 Limitations 6.2 Using Diagrams in Models to Predict Number of Citations 6.3 The Potential of Scholarly Diagrams 7 Conclusion References How Can Numerals Be Iconic? More Varieties of Iconicity 1 Introduction 2 Operational Iconicity 3 Iconicity as Resemblance 3.1 Resemblance in Qualities 3.2 Resemblance in Structure 3.3 Indirect Resemblance 4 Two New Notions of Iconicity 4.1 Exemplar Iconicity 4.2 Systematic Iconicity 5 Conclusion References Natural Deduction for Intuitionistic Euler-Venn Diagrams 1 Introduction 2 Intutionistic Euler-Venn Diagrams 3 Proof Rules References Understanding Thought Processes Observing Strategies of Drawing Data Representations 1 Introduction 1.1 Interpreting and Comprehending Graphs 1.2 Chunking in Competence Measurement 1.3 Existing Methods for the Assessment of Graph Familiarity 2 Observing Strategies of Drawing Graphs and Charts 2.1 Study 2.2 Line Graph: Results 2.3 Line Graph: Discussion 2.4 Bar Chart: Results and Discussion 2.5 Overall Discussion of the Study 3 CPM-GOMS Verification of the Line Graph Chunking 3.1 CPM-GOMS Modelling 3.2 Modelling Results 4 Discussion References Diagrams in Essays: Exploring the Kinds of Diagrams Students Generate and How Well They Work Abstract 1 Introduction 2 Method 3 Results and Discussion 3.1 Kinds of Diagrams Used to Portray Processes/Mechanisms 3.2 Ways that Diagrams Were Used Effectively 3.3 Ways that Diagrams Were Not Used Effectively 3.4 Implications for Theory, Research, and Practice Acknowledgment References How Can We Statistically Analyze the Achievement of Diagrammatic Competency from High School Regular Tests? 1 Necessity of Assessing Diagrammatic Competency in School 2 Development of Tasks to Assess Diagrammatic Competency 3 Results and Discussion References Author Index