## Visual Reasoning with DiagramsAmirouche Moktefi, Sun-Joo Shin 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. |

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### Contents

1 | |

The Geometry of Diagrams and the Logic of Syllogisms | 19 |

A Diagrammatic Calculus of Syllogisms | 33 |

Carrolls Marked Quadriliteral Diagram | 55 |

The Numerical Segment | 73 |

Diagrammatic Reasoning with Classes and Relationships | 83 |

On the Completeness of Spider Diagrams Augmented with Constants | 101 |

A PracticeBased Approach to Diagrams | 135 |

Figures Formulae and Functors | 153 |

Representation of Graphs in Diagrams of Graph Theory | 171 |

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### Common terms and phrases

AA2A abstract algebraic alleys Aristotle Aristotle’s biliteral diagram bullet symbol Carroll Carroll’s category theory classes concepts conclusion constant spider labels CRL diagrams cross every bridge CS(d define diagram d1 diagrammatic reasoning diagrams with constants distinct courses elements Euler diagrams Eulerian circuits example Existential Graphs existential import existential spiders expressivism formal free module function geometry graph theory H Isp habitat iconic K˝onig land areas Lemma Let D1 long interval Lucas mathematical recreations Mathematics Subject Classification maze metalogic middle term Moktefi n-term syllogisms negation notation number of bridges number of distinct ontologies Peirce Peirce’s philosophical Poinsot polygons possible predicate logic premises problem of dominoes proof propositions quadriliteral quadriliteral diagram relation relationship represent representation Sect semantics sentences shaded Shin spider diagrams structure syllogism syllogistic diagrams syllogistic inference syntactic syntax theorem third figure treatise of 1936 triliteral unitary diagram valid Vandermonde Venn Venn diagrams Visual Reasoning zone