This book, written by the outstanding Russian philosopher and logician A. A. Zinoviev, is devoted to the problem of logical implication, which, according to the author, is one of the central theoretical problems of modern logic. The problem of logical implication is, briefly speaking, the following: can classical propositional logic be directly considered as a general theory of inference, giving a description of the habitually clear rules of inference; If not, is it possible to construct a system for logical implication that is similar to the constructions in classical propositional logic? When studying this problem, the author appeals to an intuitive understanding of the rules of inference, to empirical data of reasoning, etc. It is recommended for philosophers, logicians, scientific methodologists, students and graduate students of relevant specialties.