Dick de Jongh on Intuitionistic and Provability Logics

ISBN-13: 9783031479205 / Angielski

Nick Bezhanishvili; Rosalie Iemhoff; Fan Yang

Spis treści

Chapter 1. Notes on my scientific life (Dick de Jongh).- Chapter 2. Lewisian fixed points I: Two incomparable constructions (Tadeusz Litak and Albert Visser).- Chapter 3. An abstract look at the fixed-point theorem for provability logic (Johan van Benthem).- Chapter 4. The Σ1-provability logic of HA revisited (Mojtaba Mojtahedi).- Chapter 5. An overview of Verbrugge semantics, a.k.a. generalised Veltman semantics (Joost J. Joosten, Jan Mas Rovira, Luka Mikec, and Mladen Vuković).- Chapter 6. Deciding dependence in logic and algebra (George Metcalfe and Naomi Tokuda).- Chapter 7. About the unification types of modal logics (Philippe Balbiani and Çiğdem Gencer).- Chapter 8. Proof theory for lax logic (Rosalie Iemhoff).- Chapter 9. Intermediate logics in the setting of team semantics (Nick Bezhanishvili and Fan Yang).- Chapter 10. Well partial orders (Andreas Weiermann).- Chapter 11. Learning to act and observe in partially observable domains (Thomas Bolander, Nina Gierasimczuk, and Andrés Occhipinti Liberman).- Chapter 12. Axiomatizing origami planes (Lev Beklemishev, Anna Dmitrieva, and Johann A. Makowsky).- Chapter 13. Bibliography of Dick de Jongh.

Blurb

This book is dedicated to Dick de Jongh’s contributions to the theory of intuitionistic and provability logics. Consisting of 12 chapters, written by leading experts, this book discusses de Jongh’s original contributions and consequent developments that have helped to shape these fields. The book begins with an autobiographic note by Dick de Jongh, which discusses the main themes of his work and places the other contributions in context. The next four chapters explore the De Jongh-Sambin fixed point theorem and other contributions to provability and interpretability logics. The following four chapters focus on modal, intuitionistic and intuitionistic modal logics. They discuss independence of formulas, unification and de Jongh formulas in intuitionistic and modal logics. Then there follow two chapters on the other two areas to which Dick de Jongh made important contributions: the theory of well-partial orders, together with Rohit Parikh, and formal learning theory. The last chapter on Origami Geometry can be seen as representing the Master of Logic program of the Institute for Logic, Language and Computation (ILLC) in which de Jongh invested a lot of energy. This volume provides a vital overview – and continuation of - de Jongh’s prolfic work in the theory of intuitionistic and provability logics.