V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics

ISBN-13: 9783031068423 / Angielski / Twarda / 2022 / 313 str.

Alex Citkin; Ioannis M. Vandoulakis

Opis

This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic.
The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics.
The book also contains an exposition of Yankov’s revolutionary approach to constructive proof theory. The editors also include Yankov’s contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

Spis treści

Chapter 1. Short autobiography (Vadim A. Yankov), Part I: Non-classical logics.- Chapter 2. V. Yankov’s contributions to propositional Logic (Alex Citkin).- Chapter 3. Dialogues and proofs; Yankov’s contribution to proof theory (Andrzej Indrzejczak).- Chapter 4. Jankov formulas and axiomatization techniques for intermediate logics (Guram Bezhanishvili, Nick Bezhanishvili).- Chapter 5. Yankov Characteristic formulas (an algebraic account) (Alex Citkin).- Chapter 6. The invariance modality (Silvio Ghilardi).- Chapter 7. The Lattice NExtS41 as composed of replicas of NExtInt, and beyond (Alexei Muravitsky).- Chapter 8. An Application of the Yankov characteristic formulas (Valery Plisko).- Chapter 9. A note on disjunction and existence properties in predicate extensions of intuitionistic logic – An application of Jankov formulas to predicate logics (Nobu-Yuki Suzuki).- Part II: History and philosophy of mathematics.- Chapter 10. On V.A. Yankov’s contribution to the history of foundations of mathematics (Ioannis M. Vandoulakis).- Chapter 11. On V.A. Yankov’s existential interpretation of the early Greek philosophy. The case of Heraclitus (Tatiana Yu. Denisova).- Chapter 12. On V.A. Yankov’s hypothesis of the rise of Greek mathematics (Ioannis M. Vandoulakis).

O autorze

A. Citkin studies for many years the theory of the Yankov characteristic formulas, their generalizations and applications in different areas of propositional, modal and algebraic logic.

I. Vandoulakis is Adjunct Professor in history and philosophy of science at the Hellenic Open University, Greece. He holds a Ph.D. in history of mathematics from Moscow M.V. Lomonosov State University (1991). He has published on history and philosophy of Greek mathematics, history of mathematical logic, philosophy and the foundations of mathematics.