Mathematical logic and algorithm theory

This textbook is dedicated to the exposition of mathematical logic and algorithm theory. The basis of the textbook consists of lectures given to second-year students of the Faculty of Computer Science at the F.M. Dostoevsky Omsk State University. It covers classical logic, resolution method, formal calculi, formal arithmetic, principles of logical programming, fuzzy logic and fuzzy arithmetic, modal, temporal, and algorithmic logics. It includes Kripke semantics, Hoare's axioms of algorithmic logic, paraconsistent logics, Vasiliev's and Lukasiewicz's logics, relevant logics. It provides insights into partially recursive functions, Turing-Post machine, Markov's normal algorithms, and algorithm complexity. For students specializing in "Computer Security," "Information Security," and "Computer Science and Engineering."