Фундаментальная силлогистика с интенсиональной точки зрения.

Abstract

We set out an intensional semantics for pure positive syllogistic language. According to it each term Q denotes not a set of individuals but a concept d(Q) considered as a non-empty set of positive or negative characters. We define a function * on concepts, which assigns to every concept a the contrary concept $\alpha^*:p_i\in\sim\alpha^*\Leftrightarrow\sim p_i\in \alpha^*$ and $\sim p_i\in\alpha^*\Leftrightarrow p_i\in \alpha$, where pt is a positive character and $\sim p_i$ is a negative character. $SaP$ means that $d(P)\subseteq d(S)$, $SeP$ means that $d(P)^*\cap d(S)\neq\varnothing$. We prove that this semantics is adequate to syllogistic system with the following axiom schemes: $(MaP\& SaM )\supset SaP$, $(MeP\& SaM )\supset SeP$, $SeP\supset PeS$, $SaS$, $SiP\equiv\neg SeP$, $SoP equiv\neg SaP$.