Overview
- Presents comprehensive exposition of theory of V. Yankov’s characteristic formulas and its contemporary developments
- Is a groundbreaking approach to the constructive proof theory
- Addresses innovative interpretation of early Greek mathematics and Philosophy
Part of the book series: Outstanding Contributions to Logic (OCTR, volume 24)
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About this book
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.
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Keywords
- Jankov Formula In Propositional Logic
- Jankov Formula In Modal Logic
- Characteristic Formula
- Frame and Subframe Formula
- Splitting Algebra
- Modal Canonical Formulas
- Pretabular Intermediate Logics
- Markov’s Constructivism
- Intuitionistic Logic
- Ultra-intuitionism
- Greek Philosophy and Mathematics.
- Yankov Formulas for Heyting Algebras
- Yankov Characteristic Formulas
- Invariance Modality
- Constructive Proofs based on Dialogical Interpretatio
- Lattice NExtS4 as a Puzzle Composed of NExtInt-Pieces
- adding Constants to FDE-based Logics
- Canonical Models and Yankov Formulas
- Lattice of Superintuitionistic Propositional Logics
Table of contents (12 chapters)
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Front Matter
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Non-Classical Logics
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Front Matter
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Back Matter
Editors and Affiliations
About the editors
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.
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.
Bibliographic Information
Book Title: V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics
Editors: Alex Citkin, Ioannis M. Vandoulakis
Series Title: Outstanding Contributions to Logic
DOI: https://doi.org/10.1007/978-3-031-06843-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-06842-3Published: 09 November 2022
Softcover ISBN: 978-3-031-06845-4Published: 10 November 2023
eBook ISBN: 978-3-031-06843-0Published: 08 November 2022
Series ISSN: 2211-2758
Series E-ISSN: 2211-2766
Edition Number: 1
Number of Pages: XI, 313
Number of Illustrations: 27 b/w illustrations
Topics: Mathematical Logic and Foundations, History of Mathematical Sciences, Logic, General Algebraic Systems