This book is dedicated to the 100th anniversary of the birth of A. V. Kuznetsov, who was born in 1926 and whose achievements laid new paths for the development of many branches of non-classical logic in the 1950s-1980s, influencing many researchers in the field to this day. Kuznetsov's formal education lasted only until the sixth grade of school, so he can be considered self-taught; however, he became one of the most prominent figures in the field of mathematical logic in the former USSR. While obtaining new results in various areas of mathematical logic, sometimes unrelated to each other, as well as in the related areas of universal algebra, he used to be quite careless about their publication. The approach taken in this book is threefold. it places Kuznetsov's well-known results in a historical perspective; second - some lesser-known results of Kuznetsov are brought to the broader English-reading audience, not only experts in the field. Third, new results that clearly bear the influence of Kuznetsov are presented.

Alex Citkin was a student of A.V. Kuznetsov and under his supervision he defended doctor thesis in mathematical logic. The main areas of Citkin's interest are intermediate logics, admissible rules, varieties and quasivarieties of Heyting (and similar to them) algebras, logical systems with rejection.  Alexei Muravitsky was a student of A.V. Kuznetsov and under his supervision he defended doctor thesis in mathematical logic. The main areas of Muravitsky's interest are non-classical propositional logics and related semantics, non-monotonic reasoning, philosophy and epistemology of logic, history of logic, applications of many-valued logic in computer science, domain theory, consequence relations and operators.