This article contains the proof of equivalence boolean algebra and syllogistics arc2. The system arc2 is obtained as a superstructure above the propositional calculus. Subjects and predicates of syllogistic functors a, E, J, O may be complex terms, Which are formed using operations of intersection, Union and complement. In contrast to negative sentences the interpretation of affirmative sentences suggests non-Empty terms. To prove the corresponding theorem we demonstrate that boolean algebra is included into syllogistics arc2 and vice versa.

Logic today is a ramified discipline existing on many levels. It is actively pursued by philosophers, mathemeticians, and computer specialists. The reason is that it is widely employed to solve a number of problems both in the theory of knowledge and in mathematics and computer science. But the broad spectrum of application of contemporary logic does not change the fact that its basic content has the nature of philosophical methodology. In contemporary logic it is the forms of thought and the (...) methods of scientific cognition, the modes of organization of scientific knowledge, and the procedures for the introduction of various concepts, abstractions, and idealizations that are studied. This places logic in intimate contact with epistemology and methodology. The distinctiveness of the approach taken by formal logic to this particular subject consists simply of its studying all these procedures pertaining to concrete cognition through the use of special formal languages, of algebraic, topological, and other exact techniques. (shrink)

Two subject-predicate calculi with equality,SP = and its extensionUSP =, are presented as systems of natural deduction. Both the calculi are systems of free logic. Their presentation is preceded by an intuitive motivation.It is shown that Aristotle's syllogistics without the laws of identitySaP andSiP is definable withinSP =, and that the first-order predicate logic is definable withinUSP =.

Монография является итогом многолетних исследований силлогистических теорий с точки зрения символической логики. Впервые ставится и исследуется проблема полноты множества логических констант в силлогистической теории. Для специалистов.