Visual Reasoning with Diagrams

Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. Recently, we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning.

Preface.- 1. What is a logical diagram? (Catherine Legg).- 2. The geometry of diagrams and the logic of syllogisms (Richard Bosley).- 3. A diagrammatic calculus of syllogisms (Ruggero Pagnan).- 4. Beyond syllogisms: Carroll’s (marked) quadriliteral diagram (Amirouche Moktefi).- 5. A diagrammatic bridge between classical and fuzzy logics (Ferdinando Cavaliere).- 6. Diagrammatic reasoning with Classes and relationships (Jørgen Fischer Nilsson).- 7. On the completeness of spider diagrams augmented with constants (Gem Stapleton, John Howse, Simon Thompson, John Taylor and Peter Chapman).- 8. A practice-based approach to diagrams (Valeria Giardino).- 9. Figures, formulae, and functors (Zach Weber).- 10. Diagrams and concepts of graph theory (Mitsuko Mizuno).