1. Introduction: Some Brief Historical and Philosophical Remarks.- 2. A Brief Introduction to Constructive Type Theory.- 3. Basic Notions for Dialogical Logic.- 4. Advanced Dialogues: Play Level.- 5. Advanced Dialogues: Strategy Level.- 6. Local Reasons and Dialogues for Immanent Reasoning.- 7. The Dialogical Roots of Equality: Dialogues for Immanent Reasoning.- 8. The Remarkable Case of the Axiom of Choice.- 9. From Dialogical Strategies To CTT-Demonstrations And Back.- 10. Material Dialogues.- 11. Concluding Remarks: A Plaidoyer for the Play Level.

Shahid Rahman is full-professor (classe exceptionnelle) of logic and epistemology at the Université de Lille-Nord-pas-de-Calais, Sciences Humaines et Sociales. He is also researcher at the UMR-CNRS 8163: STL.

Prof. Rahman works on philosophy and history of logic and the foundations of mathematics. He is the leading researcher in the field of the dialogical approach to logic. Prof. Rahman is the main editing director of two collections of books in Springer, namely, Logic, Epistemology and the Unity of Science (more than 40 volumes edited so far); and Logic, Argumentation and Reasoning, Perspectives from the Social Sciences and the Humanities. He is also main editor director of three other collections in College Publications, London. His most recent book include N. Clerbout/S. Rahman: Linking Game-Theoretical Approaches with Constructive Type Theory. Dialogical Strategies, CTT Demonstrations and the Axiom of Choice, Dordrecht, Springer, 2015; a

Ansten Klev is postdoctoral fellow at the Czech Academy of Sciences. He holds a PhD in philosophy from Leiden University. His research interests are primarily in the philsophy and history of logic and mathematics. He is especially interested in the philosophical foundations of Martin-Löf's type theory.

Zoe McConaughey is a Ph.D student in history and philosophy of logic at the Université de Lille and the Université du Québec à Montréal under the joint supervision of Shahid Rahman and Mathieu Marion; her doctoral dissertation, "La Science et l'activité du dialecticien", aims at developping Aristotle's logic within the dialogical framework of immanent reasoning in order to highlight the dialectical background of the Organon.