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This volume explores how mathematical propositions are discovered, how they are demonstrated in various mathematical cultures — ancient Greece, classical Islam, medieval and modern Europe, India, China, and pre-modern Japan — and how they are shaped in texts and stylistic traditions.The geographic range is not restricted simply to Europe and the method of demonstration is not limited to the axiomatic method, which is thought to have emerged in ancient Greece. Topics of the discussions include the visual and axiomatic modes of reasoning in ancient Greece, algebraic demonstrations...

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...