This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion.

One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning.

According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.

Proposes a new way to implement interaction in logic Provides an innovative approach on linking Martin-Löf's Constructive Type theory and Dialogical Logic Includes worked out exercises and examples

Autorentext

Shahid Rahman: 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. . Member (2016-2018) of the Conseil Scientifique du Réseau national des Maisons des Sciences de l'Homme. Member of the commission of the Institute Eric Weil, Director (for the French side) of the ANR-DFG Franco-German project 2012-2015 (Lille (MESHS)/Konstanz, Prof M. Armgardt): Théorie du Droit et Logique/Jurisprudenz und Logik. Studies: Masters in Philosophy, Mathematics, Philology (Erlangen-Nürnberg Universität) 1986-1989; PhD in Philosophy, Psychology, Philology , thesis on dialogical logic and constructive mathematics, 1990-1993; Habilitation in Philosophy (for the grade of professor), Universität des Saarlandes, 1994-1997. Professional Experience: Wissenschatlicher Mitarbeiter, Universität des Saarlandes, 1996-98. Researcher at the Max-Planck Institut für Informatik and at the Deutsches Forschungszentrum für Künstliche Intelligenz 1997-2000. Acting Director of the Department of Philosophy, Universität des Saarlandes, 1999. Prof. Rahman works span both philosophy of logic and its history, including a dialogical perspective on Constructive Type Theory. In fact, he is the leading researcher in the field of the dialogical conception of logic to which he contributed with publications in, among other fields, non-classical logics, legal reasoning, Aristotle, Arabic Logic and Epistemology. Muhammad Iqbal: Lecturer at Universitas Islam Negeri Antasari, Banjarmasin Indonesia. PhD student in philosophy at the UMR-CNRS 8163:STL., Université de Lille-Nord-pas-de-Calais, Sciences Humaines et Sociales. His main interests are, Islamic Law, Logic and Epistemology.Soufi Youcef: Lecturer at the Department of Classical, Near Eastern, and Religious Studies, University of British Columbia, BUCH C206, 1866 Main Mall, Vancouver,Canada. His interests are: Islamic Law, Islamic Legal Theory (U l al-fiqh), Medieval Juristic Disputations.

Inhalt

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. <p