Logical formalism is seen as a tool for formulating and solving meaningful problems. Its two aspects are analyzed: semantic - the establishment of the feasibility of logical functions - and syntactic - the construction of conclusions in logical calculus. The main task of the book is to highlight the so-called local tasks, which are characterized by simple procedures for both establishing feasibility and drawing conclusions. To describe these classes of problems, a matrix representation of logical formulas and operations on matrices are introduced. This representation makes it possible to see the essential properties of logical formulas that do not appear with the traditional approach. The book can be useful as a tutorial on disciplines: discrete mathematics, information modeling, artificial intelligence and expert systems design.