a theory of logical deduction that studies inferences consisting of categorical statements (judgments): the universal affirmative (every S is P), universal negative (no S is P), particular affirmative (some S are P), and particular negative (some S are not P). Syllogistic examines the deduction of a conclusion from one premise (direct inferences) and complex and compound syllogisms, or polysyllogisms, which have at least three premises. However, syllogistic emphasizes primarily the theory of the categorical syllogism, which has only two premises and one conclusion of an abovementioned type.
Aristotle, the founder of logic as a science, devised a system of classifying and validating the forms (moods) of syllogisms. Subsequently, syllogistic was refined by various schools of classical and medieval logicians, including the Peripatetics and the Stoics. Although F. Bacon, R. Descartes, J. S. Mill, and other scholars noted that syllogistic was of limited applicability, it was long an integral, traditional element of classical education in the humanities. Thus, it is often called traditional logic. With the establishment of the calculi of mathematical logic, the role of syllogistic became very modest. It was proved that by using the one-place predicate calculus, a fragment of the predicate calculus, it is possible to obtain almost the entire content of syllogistic—all deductions not dependent on the typical syllogistic assumption of an empty object field. A number of axiomatic statements of syllogistic have also been obtained in the terms of modern mathematical logic (J.Łukasiewicz, 1939).