Интенсиональная семантика традиционной силлогистики.

Abstract

We present a formal realization of Leibnitz' idea of intensional interpretation of the traditional syllogistic. We set out an intensional semantics and prove that it is adequate to Lukasiewicz' syllogistic. The core idea of this semantics is to associate with each term of a categorical statement not a set of individuals but a concept considered as a non-empty and non-contradictory set of positive or negative characters and to treat syllogistic constants as denoting intensional relations between concepts. According to this approach, ‘Every S is P' means that S contains all characters from P, ‘Some S is P ’ means that S and P don't contain contrary characters (positive and negative).