Аннотация:This article describes the building of a structural systematization of some theories of pure positive syllogistics (theories C2, PC, KC, BS, C4, C3 and C3.1). At the base of systematization are lying the order relation upon the set of all theories with the classical logic basis formulated in common language. The results of the systematization are presented in the form of a directed graph (Hasse diagram). There are constructed a number of syntactic extensions and weakenings of the classical syllogistic theories.