Традиционная силлогистика с отрицательными терминами

Abstract

We set out the following axiom schemes for traditional syllogistic with negative terms: $(MaP \& SaM) \supset SaP$, $SiP \supset PiS$, $SaS$, $SaP \supset SiP$, $SeP \equiv \neg SiP$, $SoP \equiv \neg SaP$, $SaP \equiv SeP'$, $SiP \equiv SiP''$. We prove that this system embeds into the predicate calculus by the interpretation of categorical propositions made by M. Bejanishwili and L. Mchedlishwili: $SaP \rightarrow (\exists xSx \& \exists x \neg Sx \& \exists xPx \& \exists x \neg Px) \supset \forall x (Sx \supset Px)$, $SiP \rightarrow (\exists xSx \& \exists x \neg Sx \& \exists xPx \& \exists x \neg Px) \supset \exists x (Sx \& Px)$, $SeP \rightarrow (\exists xSx \& \exists x \neg Sx \& \exists xPx \& \exists x \neg Px) \supset \forall x (Sx \supset \neg Px)$, $SoP \rightarrow (\exists xSx \& \exists x \neg Sx \& \exists xPx \& \exists x \neg Px) \supset \exists x (Sx \& \neg Px)$.