Abstract
In this paper, we study special subclasses of theories on the basis of the connection between the amalgamation property and the joint embedding property, as well as between the h-amalgamation property and the joint continuation property. Our results are presented in both the classical first-order logic and positive logic, which exhibit a parallel structure. We establish sufficient conditions under which the amalgamation property implies the joint embedding property, and conversely; the h-amalgamation property implies the joint continuation property, and vice versa. Additionally, we investigate the preservation of these subclass links under extensions of the given theory.