Syntactic Interpretation of Categorical Attributive Propositions

Abstract

In the article we propose a new type of models for categorical attributive propositions. Usually the subject and predicate of the attributive proposition are interpreted extensionally as some sets of individuals. Logical relations between subject and predicate are understood as the set-theoretic relations between their extensions. We propose a syntactic interpretation of subject and predicate of attributive propositions and interpret them as some formulas of propositional logic. These formulas can be understood as the definitions of common terms. Logical relations between subject and predicate are understood as the logical relations between their definitions. The article contains a proof that the system of fundamental syllogistic is consistent and complete with respect to the proposed semantics. Built interpretation can be generalized to other systems of syllogistic.