Why are diagrams sometimes so useful, facilitating our understanding and thinking, while at other times they can be unhelpful and even misleading? Drawing on a comprehensive survey of modern research in philosophy, logic, artificial intelligence, cognitive psychology, and graphic design, Semantic Properties of Diagrams and Their Cognitive Potentials reveals the systematic reasons for this dichotomy, showing that the cognitive functions of diagrams are rooted in the characteristic ways they carry information. In analyzing the logical mechanisms behind the relative efficacy of diagrammatic representation, Atsushi Shimojima provides deep insight into the crucial question: What makes a diagram a diagram?

This book constitutes the refereed proceedings of the 15th International Conference on the Theory and Application of Diagrams, Diagrams 2026, held in Tallinn, Estonia, during August 25–28, 2026.The 14 full papers, 20 short papers and 9 posters included in this book were carefully reviewed and selected from 57 submissions. They were organized in topical sections as follows: Logical Diagrams; Mathematical Diagrams; Diagrams and Cognition; Diagrams and Computation; and Applications.

This book constitutes the refereed proceedings of the 15th International Conference on the Theory and Application of Diagrams, Diagrams 2026, held in Tallinn, Estonia, during August 25–28, 2026.The 14 full papers, 20 short papers and 9 posters included in this book were carefully reviewed and selected from 57 submissions. They were organized in topical sections as follows: Logical Diagrams; Mathematical Diagrams; Diagrams and Cognition; Diagrams and Computation; and Applications.

Although diagrammatic representations have been a feature of human com- nication from early history, recent advances in printing and electronic media technologyhaveintroducedincreasinglysophisticatedvisualrepresentationsinto everydaylife. We need to improve our understanding of the role of diagramsand sketches in communication, cognition, creative thought, and problem-solving. These concerns have triggered a surge of interest in the study of diagrammatic notations, especially in academic disciplines dealing with cognition, compu- tion, and communication. We believe that the study of diagrammatic communication is best pursued as an interdisciplinary endeavor. The Diagrams conference series was launched to support an international research community with this common goal. After successful meetings in Edinburgh (2000) and Georgia (2002), Diagrams 2004 was the third event in the series. The Diagramsseries attracts a largenumber of researchersfrom virtually all academic?elds who arestudying the nature of d- grammatic representations,their use in human communication, and cognitive or computationalmechanismsforprocessingdiagrams.Bycombiningseveralearlier workshop and symposium series that were held in the US and Europe - R- soning with Diagrammatic Representations (DR), US; Thinking with Diagrams (TWD), Europe; and Theory of Visual Languages (TVL), Europe - Diagrams has emerged as a major international conference on this topic.

Why are diagrams sometimes so useful, facilitating our understanding and thinking, while at other times they can be unhelpful and even misleading? Drawing on a comprehensive survey of modern research in philosophy, logic, artificial intelligence, cognitive psychology, and graphic design, Semantic Properties of Diagrams and Their Cognitive Potentials reveals the systematic reasons for this dichotomy, showing that the cognitive functions of diagrams are rooted in the characteristic ways they carry information. In analyzing the logical mechanisms behind the relative efficacy of diagrammatic representation, Atsushi Shimojima provides deep insight into the crucial question: What makes a diagram a diagram?

This book constitutes the refereed proceedings of the 15th International Conference on the Theory and Application of Diagrams, Diagrams 2026, held in Tallinn, Estonia, during August 25–28, 2026.The 14 full papers, 20 short papers and 9 posters included in this book were carefully reviewed and selected from 57 submissions. They were organized in topical sections as follows: Logical Diagrams; Mathematical Diagrams; Diagrams and Cognition; Diagrams and Computation; and Applications.

This book constitutes the refereed proceedings of the 15th International Conference on the Theory and Application of Diagrams, Diagrams 2026, held in Tallinn, Estonia, during August 25–28, 2026.The 14 full papers, 20 short papers and 9 posters included in this book were carefully reviewed and selected from 57 submissions. They were organized in topical sections as follows: Logical Diagrams; Mathematical Diagrams; Diagrams and Cognition; Diagrams and Computation; and Applications.

Although diagrammatic representations have been a feature of human com- nication from early history, recent advances in printing and electronic media technologyhaveintroducedincreasinglysophisticatedvisualrepresentationsinto everydaylife. We need to improve our understanding of the role of diagramsand sketches in communication, cognition, creative thought, and problem-solving. These concerns have triggered a surge of interest in the study of diagrammatic notations, especially in academic disciplines dealing with cognition, compu- tion, and communication. We believe that the study of diagrammatic communication is best pursued as an interdisciplinary endeavor. The Diagrams conference series was launched to support an international research community with this common goal. After successful meetings in Edinburgh (2000) and Georgia (2002), Diagrams 2004 was the third event in the series. The Diagramsseries attracts a largenumber of researchersfrom virtually all academic?elds who arestudying the nature of d- grammatic representations,their use in human communication, and cognitive or computationalmechanismsforprocessingdiagrams.Bycombiningseveralearlier workshop and symposium series that were held in the US and Europe - R- soning with Diagrammatic Representations (DR), US; Thinking with Diagrams (TWD), Europe; and Theory of Visual Languages (TVL), Europe - Diagrams has emerged as a major international conference on this topic.