Арифметическая семантика для нетрадиционных систем силлогистики.

Abstract

Leibniz worked out fo r the assertoric positive syllogistics an arithmetical sem antics with ordered pairs o f mutually prim e natural numbers as adm itted values o f term-variables. In [5], [14] was proved that the arithm etical semantics gives the adequate understanding o f the Lukasiewicz's form a l Systems L o f syllogistics. In set-theoretical (extensional) sem antics o f the fo r mal Systems В and Sm, in contrary to L, the empty value fo r term -variables is adm itted and the propositions $SaP$ and $SeP$ means accordingly $S\subseteq P$ and $S\cap P=\varnothing$ (in B), $S\neq\varnothing\& S\subseteq P$ and $S\cap P=\varnothing$ (in Sm). In this article is defined Leibniz-style arithm etical semantics with arbitrary natural numbers as adm itted values o f term-varibles fo r these systems.