Фундаментальная силлогистика с неопределенно-местной константой.

Abstract

The paper concerns the problem of the representation of all possible extensional relations among any finite list of the universal terms by means of positive syllogistic - syllogistic without negative and other complex terms. I introduce new syllogistic constant @ with indefinite arity. The atomic formulae are of the type $S_1S_2...S_n@P_1P_2...P_m$, where $n+m> 1$, complex formulae are constructed by means of the propositional connectives. I offer the following translation * from the syllogistic language into the language of predicate calculus: $(S_1S_2...S_n@P_1P_2...P_m)^*=\neg\exists(S_1x\& S_2x\&...\& S_nx\&\neg P_1x\&\neg P_2x\&...\&\neg P_mx),(\neg A)^*=\neg A^*, (A\triangledown B)^*=A^*\triangledown B^*$, where $\triangledown$ is any binary connective. I formulate a syllogistic system which is the generalization of the fundamental positive syllogistic and prove that it is embedded into the classical predicate calculus under the translation *.