Contents: Jean-Yves Beziau/Gillman Payette: Preface - Volker Peckhaus: Algebra of Logic, Quantification Theory, and the Square of Opposition - Yurii Khomskii: William of Sherwood, Singular Propositions and the Hexagon of Opposition - John N. Martin: Existential Commitment and the Cartesian Semantics of the Port-Royal Logic - Juan M. Campos-Benítez: The Medieval Modal Octagon and the S5 Lewis Modal System - Alessio Moretti: From the "Logical Square" to the "Logical Poly-Simplexes" - Jonathan Westphal: The Application of Vector Theory to Syllogistic Logic - Sumanta Sarathi Sharma: Interpreting Squares of Oppositions with the Help of Diagrams - Dag Westerståhl: Classical vs. Modern Squares of Opposition, and Beyond - Pieter A. M. Seuren: From Logical Intuitions to Natural Logic - Fabien Schang: Questions and Answers about Oppositions - Peter Schroeder-Heister: Definitional Reasoning in Proof-Theoretic Semantics and the Square of Opposition - Régis Angot-Pellissier: 2-Opposition and the Topological Hexagon - Corina Strössner/Niko Strobach: Veridications and their Square of Opposition - Laurence R. Horn: Histoire d' O: Lexical Pragmatics and the Geometry of Opposition - Sémir Badir: How the Semiotic Square Came - Ivana Bianchi/Ugo Savardi: The Cognitive Dimensions of Contrariety - Sieghard Beller: Human Deontic Reasoning in the Deontic Square - Antoine Seilles/Jean Sallantin: n-Opposition Theory to Structure Debates.