Diagrammatic Representation and Inference

Name: Diagrammatic Representation and Inference | 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings
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10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings

Peter Chapman Gem Stapleton Amirouche Moktefi Sarah Perez-Kriz Francesco Bellucci(Editor)

Springer (Publisher)

Published on 7. June 2018

XVI, 831 pages

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978-3-319-91376-6 (ISBN)

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Content

Intro
Preface
Organization
Contents
Keynote Contributions
Diagrams and Nonmonotonic Logic: What Is the Cognitive Relation?
References
The Beauty of Graphs
1 Introduction
References
Tutorials
Were ``Super-Turing'' Diagrammatic Reasoning Mechanisms Ancient Products of Biological Evolution?
1 Introduction
References
Using Verbal Protocols to Support Diagram Design
Abstract
1 Overview
2 Background
References
Peirce on Diagrammatic Reasoning and Semeiotic
Abstract
1 Introduction: Peirce's Early Algebraic Logic
References
Picturing Quantum Processes
1 Rationale
2 References
References
Carroll Diagrams: Design and Manipulation
Abstract
1 Introduction
2 Carroll Diagrams
3 Directions
4 Organization and Practicalities
References
Generating and Drawing Euler Diagrams
Generating Effective Euler Diagrams
1 Introduction
2 Euler Diagrams: Background
3 Euler Diagrams
4 The iCurves Euler Diagram Generation Technique
4.1 Drawing Curves in Euler Diagrams
4.2 Producing a Decomposition
4.3 Drawing Algorithm
5 Evaluation
6 Conclusion and Future Work
References
Variational Pictures
1 Introduction
2 Representing Variational Pictures
2.1 A Formal Model of Variation
2.2 Plain Pictures
2.3 Adding Choices to Pictures
2.4 Variability Types
2.5 Variability Regions
2.6 Distilling Variational Pictures
3 Properties of Variational Pictures
4 Maintenance of Variational Pictures
5 Variational Area Trees
6 Related Work
7 Conclusions and Future Work
References
Edge Label Placement in Layered Graph Drawing
1 Introduction
2 Layer Selection
3 Label Side Selection
3.1 Same-Side Strategy
3.2 Directional Strategy
3.3 On-Edge Strategy
4 Directional Decorators
5 Evaluation
6 Conclusion
References
Generation of Kolam-Designs Based on Contextual Array P Systems
1 Introduction
2 Preliminaries
3 Contextual Array P System and ``Kolam'' Pattern Generation
3.1 ``Kolam'' Generation Using PCAP
4 Concluding Remarks
References
Diagrams in Mathematics
Visual Algebraic Proofs for Unknot Detection
1 Introduction
2 Groups Induced by a Knot Diagram
3 Reading Tangles
3.1 The Theory of Reading Tangles
4 Untangling: The Main Result and an Example
5 Manipulating Tangle Diagrams with the Computer
6 Automated Proofs
7 Conclusion and Future Work
References
A Typology of Mathematical Diagrams
Abstract
1 Introduction: Why Classify Mathematical Diagrams from a Cognitive Perspective
2 Mathematical Diagrams and Figures
2.1 A Classification Scheme
2.2 Applying the Scheme
3 Examples
3.1 Prototypical Diagrams
3.2 Is This a Diagram?
3.3 What Kind of Diagram Is This? Examples that Challenge the Classification Scheme
4 Discussion: Balancing the Resolution of Diagram Classification
5 Conclusion
References
The Classificatory Function of Diagrams: Two Examples from Mathematics
1 Introduction: Diagrams and Classifications
2 The Classification of Compact Surfaces
2.1 First Classification
2.2 Dyck's Classification
2.3 The ``Fundamental Polygon''
3 An Example from Algebra: Complex Semisimple Lie Algebras
3.1 Root Systems and the Classification of Simple Lie Algebras
3.2 Artin's Presentation
3.3 Dynkin Diagrams
4 Discussion
5 Conclusions
References
Mathematical Pictures
Abstract
1 Introduction
2 Macbeth's Challenge
3 A Pragmatic Account of Pictures
4 Context and Interpretation
5 Conclusions
Acknowledgements
References
Impact and Prevalence of Diagrammatic Supports in Mathematics Classrooms
Abstract
1 Introduction
1.1 Perceptual Learning in Mathematics
1.2 Diagrammatic Supports
1.3 Implementing Supports in Practice
1.4 The Present Studies
2 Study 1
2.1 Method
2.2 Results
3 Study 2
3.1 Method
3.2 Results
4 General Discussion
References
What Sort of Information-Processing Machinery Could Ancient Geometers Have Used?
1 Introduction
2 Why Is Non-empirical Knowledge of Non-contingent Truths Important?
3 Meta-Level Competences
4 Back to Ancient Mathematical Reasoning/Discovery
5 Towards a Super-Turing Geometric Reasoner
6 Conclusion
References
Interpreting Diagrammatic Reasoning - Between Empiricism and Realism
Abstract
1 Introduction
2 Diagrams in Geometry
3 Diagrams in Mathematics and Quasi-empiricism
4 Towards a Positive Realist Account of Diagrammatic Reasoning
References
Diagram Design, Principles and Classification
Picturing Science: Design Patterns in Graphical Abstracts
1 Introduction
2 Related Work
3 GA Sample and Coding Process
4 The GA Design Space
5 Design Patterns
5.1 Layout
5.2 Depiction of Time
5.3 Text Usage
5.4 Representational Genre
6 Discussion
6.1 Scope and Results
6.2 Ambiguity in the Design of GAs
6.3 Toward Mixed-Initiative GA Design Tools
7 Conclusion
References
A Framework for Analyzing and Designing Diagrams and Graphics
Abstract
1 Introduction
2 Graphic Relationships Between Graphic Components
3 Modes of Visual Encoding, Depiction, and Correspondence
4 Mode of Visual Encoding
5 Mode of Correspondence
6 Mode of Depiction
7 Conclusions
References
A Classification of Infographics
Abstract
1 Introduction
2 Prior Research
3 Methodology
3.1 Materials
3.2 Experimental Procedure
3.3 Data Analysis
4 Results
5 Discussion
6 Conclusion
Acknowledgements
Appendix: The Infographics Classification Tree
References
Diagrammatic Maps of the New York Subway: An Historical Perspective
Abstract
1 Introduction
2 Findings
3 Conclusion
Acknowledgement
References
Sonifying Napoleon's March by Identifying Auditory Correlates of the Graphic-Linguistic Distinction
1 Translation from Graphics to Text for Accessibility
2 Identifying Auditory Correlates of the G-L Distinction
2.1 2D vs. Sequential, Analog vs. Digital and Intrinsic vs. Extrinsic
2.2 Relation Symbols and Object Symbols
3 Conclusion
References
Towards a Typology of Diagrams in Linguistics
1 Diagrams and Linguistics
2 Linguistic Parameters
3 Diagrammatic Parameters
4 Illustrating and Applying the Parameters
5 Conclusions and Future Work
References
Reasoning with Diagrams
Accessible Reasoning with Diagrams: From Cognition to Automation
1 Introduction
2 Concept Diagrams: Background and Overview
3 iCon: A Concept Diagrams Interactive Theorem Prover
3.1 Reasoning Engine
3.2 Graphical User Interface
4 Empirical Experiment for the Design of Inference Rules
4.1 Method
4.2 Results
4.3 Discussion
5 Inference Rules: Design and Implementation Guidelines
6 Related Work and Evaluation
7 Conclusion and Future Work
References
Using Diagrams to Reason About Biological Mechanisms
Abstract
1 Introduction
2 Using Question Marks in Mechanism Diagrams
3 Computationally Annotated Mechanism Diagrams
4 Finding Patterns in Large Networks to Make Inferences About Mechanisms
5 Implications
Acknowledgement
References
A Survey and Evaluation of Diagrams for Navya-Nyaya
1 Introduction
2 Methodology
3 The Basic Terms and Concepts of Navya-Nyaya
4 The Diagrams of Navya-Nyaya
5 Conclusion
References
Operations on Single Feature Indicator Systems
1 Introduction
2 The General Picture
3 Single Feature Indicator Systems
3.1 The Structure of the Target Domain
3.2 Designing the Source Representation
3.3 Semantic Conventions
4 Notation
5 Operations: Subject Union
6 Operations: Value Multiplication
7 Operations: Neutralization
8 Operations: Conditionalization
9 Operations: Uplifting
10 Operations: System Combination and Elimination
11 Conclusion
References
The Observational Advantages of Euler Diagrams with Existential Import
1 Introduction
2 Observation and Meaning-Carriers
3 Set Theory and Euler Diagrams with Existential Import
3.1 Euler Diagrams with Existential Import
3.2 Set-Theoretic Sentences
3.3 Semantic Relationships
4 Model Theory: Euler Diagrams with Existential Import
5 Model Theory: Set-Theoretic Sentences
6 Observational Completeness
7 Discussion
8 Conclusion
References
Observational Advantages: A Philosophical Discussion
Abstract
References
`Diagrams': A Hybrid Visual Information Representation and Reasoning Paradigm Towards Video Analysis
1 Introduction
2 Related Work and Motivation
3 `Diagrams': The Proposed Methodology
4 Application: An Example with Evaluation Details
5 Conclusion
References
Diagrammatic Definitions of Causal Claims
1 Introduction
2 System Semantics for Causal Claims
3 A Diagrammatic Definition
4 Sometimes and Partial Causation
5 Modelling an Agent's Interaction
6 Conclusion
References
Arcform
Abstract
1 Introduction
2 Objects and Thoughts
3 First Order Thoughts
4 Higher Order Thoughts
5 Natural-Language-Like
6 Arcform Maps
7 Unitokenality
8 Additional Features
9 Discussion
References
Euler and Venn Diagrams
Euler Diagrams Through the Looking Glass: From Extent to Intent
1 Introduction
2 Syntax and Semantics
3 Sets of Individuals and Their Attributes
4 From Extensional to Intensional Diagrams
5 From Intensional to Extensional Diagrams
6 Conclusion
References
Rigor and the Context-Dependence of Diagrams: The Case of Euler Diagrams
1 Introduction
2 Presentation of Euler's Scheme
3 The Problem
4 Hammer and Shin's Diagnosis
5 Another Analysis of Euler's Practice
6 Making it Precise: Heterogeneous Inference Rules
7 The Drawbacks of Euler's Approach and the Later History of Logical Diagrams
8 General Lessons
References
Investigating Diagrammatic Reasoning with Deep Neural Networks
1 Introduction
2 Background
2.1 Neural Networks
2.2 Euler Diagrams
3 Neural Network Architecture
3.1 Euler-Net for Categorical Output
3.2 Euler-Net for Diagram Generation
4 Evaluation
5 Discussion
6 Conclusion
References
Sequent Calculus for Euler Diagrams
1 Introduction
2 Euler Diagrams
3 Sequent Calculus
4 Discussion
References
Empirical Studies and Cognition
Metro Map Colour-Coding: Effect on Usability in Route Tracing
Abstract
1 Introduction
1.1 Basic Concepts and Nomenclature
1.2 Usability
2 Method
3 Results
4 Discussion
4.1 Navigational Hazards
4.2 Implications for Design
4.3 Implications for Automated Design
4.4 Implications for Further Research
5 Conclusions
Acknowledgement
References
The Effect of Graphical Format and Instruction on the Interpretation of Three-Variable Bar and Line Graphs
1 Introduction
2 Factorial Research Designs
3 The Effect of Training on Statistical Reasoning
4 Method
4.1 Participants
4.2 Materials
4.3 Design and Procedure
4.4 Scoring
5 Results
6 Discussion
7 Summary and Recommendations
References
Read It This Way: Scaffolding Comprehension for Unconventional Statistical Graphs
Abstract
1 Introduction
1.1 Cognitive Aids for Graph Comprehension
1.2 Prior Knowledge and Graphical Sensemaking
1.3 The Triangular Model of Interval Relations
1.4 The Present Studies
2 Study 1: Observing Learning of an Unconventional Graph
2.1 Methods
2.2 Study One: Results
2.3 Discussion of Study One
3 Study Two: Testing Scaffolds for an Unconventional Graph
3.1 Methods
3.2 Results: The Graph Reading Task
3.3 Results: The Graph Drawing Task
3.4 Discussion of Study Two
4 General Discussion
Acknowledgements
References
Rediscovering Isotype from a Cognitive Perspective
Abstract
1 Introduction: Isotype as Conceptualized by Otto Neurath
1.1 Design of Isotype
1.2 Effects of Isotype
2 A Cognitive Model of Isotype Reception
2.1 Countability Effect
2.2 Iconicity Effect
2.3 Ancillary Semantic Information
2.4 Aesthetic Preference
3 Discussion and Roadmap for Further Research
References
Perceptual Processing and the Comprehension of Relational Information in Dynamic Diagrams
Abstract
1 Introduction
1.1 Composing Relations
2 Partitioned Perceptual Processing
3 Elaborating the APM and Improving Effectiveness
3.1 Elaborating APM Stages 2 and 3
3.2 Intervening to Improve Conventionally Designed Animations
4 Discussion and Conclusion
References
Visualizing Conversational Structure: Effects of Conversation-Analytical Knowledge and Social Media Experience
1 Introduction
2 Method
2.1 Participants: Recruitment and Description
2.2 Design and Procedure
2.3 Materials and Coding
3 Results
3.1 Visualization Process and Products
3.2 RQ2: Effects of Prior Knowledge on Model Type and Tuple
4 Discussion
References
Comparing and Contrasting Within Diagrams: An Effective Study Strategy
Abstract
1 Introduction
1.1 Comparing and Contrasting as a Study Strategy
2 Method
2.1 Participants
2.2 Measure
2.3 Intervention Materials
2.4 Procedure
2.5 Data Analysis
3 Results
3.1 Differences Between Those Accessing CC DIA and not Accessing
4 Discussion
4.1 From Basic to Applied Research on Learning from Diagrams
References
The Role of Top-Down Knowledge in Spatial Cueing Using Hierarchical Diagrams
1 Introduction
1.1 The Global Structure and Local Components of Hierarchical Diagrams
1.2 Effects of the Conventional Knowledge on Spatial Attention to Hierarchical Diagrams
2 Experiment
2.1 Method
2.2 Results
2.3 Discussion
3 Conclusion
References
Exploring the Relationship Between Visual Context and Affect in Diagram Interpretation
Abstract
1 Background and Introduction
2 Study 1
2.1 Method
2.2 Themes and Outcomes
2.3 Discussion
3 Study 2
3.1 Method
3.2 Themes and Outcomes
3.3 Discussion
4 General Discussion and Conclusions
References
Visualising Latent Semantic Spaces for Sense-Making of Natural Language Text
1 Introduction
1.1 Related Work
2 LSA Model Construction
3 Interface Design
3.1 Hierarchically-Clustered Scatterplot
3.2 Heatmap Matrix: Helping Users Navigate Between Dimensions
3.3 Word Cloud
3.4 Graphical Expansion History
4 User Study
4.1 Experiment Design and Procedure
4.2 Results
5 Conclusion
References
How Users Transform Node-Link Diagrams to Matrices and Vice Versa
1 Introduction
2 Related Work
3 Empirical Evaluation
4 Results
5 Discussion
6 Conclusion
References
Peirce and Existential Graphs
Peirce and Proof: A View from the Trees
Abstract
References
A Weakening of Alpha Graphs: Quasi-Boolean Algebras
1 Introduction
2 The Logic of Quasi-Boolean Algebras
3 A Graphical System for qBas
4 Soundness and Completeness
5 Application and Discussion
6 Concluding Remarks
References
Assertive and Existential Graphs: A Comparison
1 Introduction
2 Assertions in Graphs
2.1 Intuitionistic Assertive Graphs (AGs)
2.2 Classical Assertive Graphs (CLAG)
3 Intuitionistic Existential Graphs (GrIn)
3.1 The Language of Intuitionistic Graphs
3.2 Rules
4 A Notational Comparison of Conditionals, Polarities and the Sheets of Assertion
4.1 Comparing Three Graphical Representations of Conditionals
4.2 Comparing Polarity
4.3 Comparing the Meaning of the Sheets
5 Conclusion
References
On the Transformation Rules of Erasure and Insertion in the Beta Part of Peirce's Existential Graphs
1 Diagrammatical Representations
2 Roberts' Reading
3 Dots
4 Symmetric Arrangement
5 Conclusion
References
Existential Graphs as a Basis for Structural Reasoning
Abstract
1 Introduction: Peirce's Iconic Conception of Deduction
2 Peirce's Existential Graphs and the Scroll
3 Structural Reasoning
4 A Diagrammatic Interpretation of Logical Constants
5 Conclusions and Final Remarks
References
Multiple Readings of Existential Graphs
Abstract
1 Shin's Argument
2 Objection to Shin's Argument
3 Comparison of EG and 2SL with 4SL
4 Comparison of EG with 2SL
5 Conclusion
References
Logic and Diagrams
Towards a Proof Theory for Heterogeneous Logic Combining Sentences and Diagrams
1 Introduction
2 Syntax of Heterogeneous Logic
3 Inference Rules of Heterogeneous Logic
3.1 Natural Deduction Rules for FOL
3.2 Heterogeneous Rules
4 Normalization of Heterogeneous Proofs
4.1 Normal Proof and Normalization in FOL
4.2 Reduction Rules for Heterogeneous Proofs
4.3 Normalization
4.4 Characterization of Normal Heterogeneous Proofs
5 Discussion and Future Work
References
Iconic Logic and Ideal Diagrams: The Wittgensteinian Approach
1 Introduction
2 The Case for the WIL Approach
3 Logical Proofs
4 Ideal Diagrams I - Propositional Logic
5 Ideal Diagrams II - First-Order Logic
6 Application of Logic - The Question of Adequate Formalization
7 Application of Logic - The Question of Decidability
8 Wittgenstein and Peirce
References
Aristotelian and Duality Relations Beyond the Square of Opposition
1 Introduction
2 Aristotelian and Duality Squares
3 (In)dependence of Aristotelian and Duality Diagrams
4 Octagons for Composed Operator Duality
4.1 The Buridan Octagon in Modal Syllogistics
4.2 The Lenzen Octagon in S4.2
5 Octagons for Generalized Post Duality
5.1 The Keynes-Johnson Octagon in Syllogistics with Subject Negation
5.2 The Moretti Octagon in Propositional Logic
6 Conclusion
References
Syllogistic with Jigsaw Puzzle Diagrams
1 Introduction
2 Logic and Diagrams
2.1 Logical Systems
2.2 Diagrams
2.3 Logic with Diagrams
3 Syllogistic and Jigsaw Puzzles
3.1 General Aspects of Syllogistic
3.2 General Aspects of Jigsaw Puzzles
4 The System JGSW
4.1 Elements of JGSW
4.2 Equivalence Rules
4.3 Decision Procedure
4.4 Validity of the Syllogisms
4.5 Examples
5 Properties of JGSW
5.1 Representational Properties
6 Conclusions
References
Diagrammatically Formalising Constraints of a Privacy Ontology
1 Introduction
2 3CR: A Privacy Ontology
3 Concept Diagrams
4 Reifying and Implementing 3CR+
5 Related Work
6 Conclusion
References
On Diagrams and General Model Checkers
1 Introduction
2 Graphical Specification: Basic Ideas
3 Graphical Concepts and Constructions
4 Graphical Formulations of Semantics
5 General Converter and Model-Checker
6 Concluding Remarks
References
Depicting the Redundancy of Fourth Figure Using Venn-Peirce Framework
1 Introduction
2 The (In)significance of Fourth Figure
3 The Significance of Fourth Figure
3.1 Valid Moods in Four Figures (Traditional)
3.2 Valid Moods in Four Figures (Modern)
4 Venn-Peirce Framework
4.1 Summary and Findings
4.2 Argument Against the Fourth Figure
5 Conclusion
References
Posters
Towards Diagram-Based Editing of Ontologies
1 Introduction
2 Adding Interactivity to Linear Diagrams
3 Next Steps - Heterogeneous Reasoning
References
Diagrams Including Pictograms Increase Stock-Flow Performance
Abstract
1 Introduction
2 Method
3 Results
4 Discussion
References
A Simple Decision Method for Syllogistic
1 Introduction
2 The Basics of the Method
3 Existential Import
4 Applications
References
Wallis's Use of Innovative Diagrams
1 Introduction
2 Defining the Conics: From the Cone to Algebraic Equations
3 The Arithmetical Quadrature of the Parabola
4 Concluding Remarks
References
Venn Diagram and Evaluation of Syllogisms with Negative Terms: A New Algorithm
1 Introduction
2 Algorithmic Procedure
2.1 Step I: Valuation
2.2 Step II: Propagation Rules
2.3 Step III: Interpreting the Result of the Valuations
3 Conclusion and Possible Extensions
References
Making Sense of Schopenhauer's Diagram of Good and Evil
Abstract
1 Introduction
2 Schopenhauer's Diagram
3 Diagrams for a High Number of Terms
4 The Route to Good and Evil
5 Conclusion
References
How Cross-Representational Signaling Affects Learning from Text and Picture: An Eye-Tracking Study
Abstract
1 Theoretical Framework
2 Method
3 Data Analyses and Expected Results
Acknowledgments
References
Effect of Handedness on Mental Rotation
Abstract
1 Introduction
2 Method
3 Results and Discussion
4 Conclusion
References
Euler Box Diagrams to Represent Independent and Non-independent Events
Abstract
1 Introduction
2 The Euler Box Diagram
2.1 Example: Independent Events
2.2 Example: Euler Boxes for Non-independent Events
3 Future Directions
References
A Symmetry Metric for Graphs and Line Diagrams
1 Introduction
2 Background
3 Symmetry Metric
4 Conclusion
References
Wrapping Layered Graphs
1 Introduction
2 Wrapping Layered Graphs
2.1 Heuristics
3 Results
References
Diagrams, Musical Notation, and the Semiotics of Musical Composition
Abstract
1 The Concept of Diagram in Charles S. Peirce
2 The Diagram in Beethoven's Sehnsucht
3 Final Remarks
References
Calculus CL as Ontology Editor and Inference Engine
Abstract
1 Introduction
2 Calculus CL as Ontology Editor
2.1 Arrows Depicting Theorems
2.2 Properties
3 Calculus CL as Inference Engine
3.1 Example 1 (E1)
3.2 Example 2 (E2)
References
Moded Diagrams for Moded Syllogisms
1 Introduction
2 TFL
3 Conclusions
References
A Review of Murner's Cards for Syllogistic
1 Introduction
2 Murner's Cards
3 Murner's Syllogistic
4 Conclusions
References
Towards Executable Representations of Social Machines
1 Introduction
2 Design Method
3 Diagram Language
3.1 From Diagrams to Executable Systems
4 Discussion and Conclusions
References
Transforming Storyboards into Diagrammatic Models
Abstract
1 Introduction
2 The Digital Transformation Scenario
3 Developing the Scene2Model Service Environment
4 Applying the Scene2Model Service
Acknowledgement
References
Logical Reasoning with Object Diagrams in a UML and OCL Tool
1 Introduction
2 Solving and Representing Logical Reasoning Problems
3 Conclusion and Future Work
References
Scanning the Invisible: Framing Diagrammatic Cognition in Experimental Particle Physics
Abstract
1 Introduction and Methodology
2 Case Study: Visualizing Particles by Diagrammatic Operations
3 Cognitive Imagery Projection-Manipulation Underlying Diagrammatic Operations
4 Diagrammatic Cognition in Bubble Chambers Experiments
4.1 Radius Location and Right Angle Rotation (Fig. 1 Left)
4.2 Translation of Tangents and Parallelogram Construction (Fig. 1 Center)
4.3 Diagonal Prolongation and Vertex Intersection (Fig. 1 Right)
5 Conclusion
References
Teaching Argument Diagrams to a Student Who Is Blind
Abstract
References
Correction to: How Cross-Representational Signaling Affects Learning from Text and Picture: An Eye-Tracking Study
Correction to: Chapter "How Cross-Representational Signaling Affects Learning from Text and Picture: An Eye-Tracking Study" in: P. Chapman et al. (Eds.): Diagrammatic Representation and Inference, LNAI 10871, https://doi.org/10.1007/978-3-319-91376-6_68
The Role of Diagrams in Contemporary Mathematics: Tools for Discovery?
Abstract
References
Unveiling Darwin's Theory of Evolution Through the Epistemological Study of His Diagram
Abstract
1 Introduction
2 Symbolic System and Diagrammatic Representation
3 Epistemological Analysis of Darwin's Diagram
4 Conclusion
References
Can a Picture Prove a Theorem? Using Empirical Methods to Investigate Diagrammatic Proofs in Mathematics
1 Background
2 Methods
3 Findings
References
Otto Neurath's Isotype and C. K. Ogden's Basic English
References
Diagrammatic Approaches in Computational Musicology: Some Theoretical and Philosophical Aspects
Abstract
1 The Transformational Approach in Music Analysis
2 Towards a Diagrammatic and Category-Based Music Cognition
References
Fruitful Over-Determination in Knot Diagrams
References
The Epistemology of Mathematical Necessity
Abstract
1 Introduction
2 Hume's Legacy and Its Challenges
3 A Peircean Approach
References
The Central Role of Diagrams in Algebraic Topology
Abstract
1 Introduction
2 Homotopy and Homology Theory
Acknowledgments
References
Can Spontaneous Diagram Use be Promoted in Math Word Problem Solving?
Abstract
1 Introduction
2 Method
3 Results and Discussion
References
Cognitive Control as an Underpinning of Relational Reasoning from Diagrams
Abstract
1 Introduction
1.1 Empirical Trajectories of Children Learning from Geometric Diagrams
1.2 Model Description
2 Computational Simulations of Learning Trajectories
3 Summary
References
Intersemiotic Translation: Transcreation and Diagrams
Abstract
1 What Is the Role of Intersemiotic Translation for Discovery?
2 Intersemiotic Translation as Operational Icon
3 The Intersemiotic Translation of the Fachwerkhäuser des Siegener Industriesgebietes and the Models of Iconic Semiosis
4 Conclusion
References
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Diagrammatic Representation and Inference

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