This book is dedicated to V.A. Yankovs 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 Yankovs 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 Yankovs revolutionary approach to constructive proof theory. The editors also include Yankovs 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.
Chapter
1. Short autobiography (Vadim A. Yankov), Part I: Non-classical
logics.
Chapter
2. V. Yankovs contributions to propositional Logic (Alex
Citkin).
Chapter
3. Dialogues and proofs; Yankovs 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. Yankovs contribution to the history of foundations of
mathematics (Ioannis M. Vandoulakis).
Chapter
11. On V.A. Yankovs
existential interpretation of the early Greek philosophy. The case of
Heraclitus (Tatiana Yu. Denisova).
Chapter
12. On V.A. Yankovs hypothesis
of the rise of Greek mathematics (Ioannis M. Vandoulakis).
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.
