Позитивные силлогистики васильевского типа.

Abstract

The famous Russian logician N.A. Vasiliev in his article "About Particular Statements, Triangle of Oppositions and the Law of Excluded Forth" proposed to found the logic of syllogistic type on the ground of three kinds of propositions: a, e and the so called accidental propositions "Only some (not all) S are P". In this paper we try to reconstruct in Vasiliev's style three well-known syllogistic systems: fundamental Brentano-Leibnitz syllogistic, positive syllogistic fragment of Bolzano’s logic and traditional syllogistic formalized by Lukasiewicz. The modification of the last system can be regarded as an adequate formalization of Vasiliev's assertoric syllogistic, because all syllogistic principles accepted by Vasiliev are provable in it.