<p>The paper investigates the non-Fregean approach in studying logical relationships between propositional logics. Central to this approach is the rejection of the so-called Frege’s Principle, according to which sentences are names of their truth values. Instead, the non-Fregean paradigm introduces a universe of semantic correlates of sentences to the semantics and a new connective of a non-Fregean equivalence to the language, resulting in a system that enables us to reason not only about the logical values of sentences but also about their semantic references. In this paper, we study various non-Fregean logics, including the classical Suszko’s logics with the identity connective and Grzegorczyk’s logics of description with the connective of equimeaning, as well as several non-classical non-Fregean logics. We show that the well-known non-classical propositional logics, such as modal, three-valued, intuitionistic, paraconsistent, and relevant logics, are either non-Fregean or can be extended to non-Fregean logics of greater expressive power. The main result is a comprehensive map of logical dependencies among the logics under consideration. Our results reveal that the non-Fregean approach offers a unified and inclusive framework to study similarities and differences between various propositional logics, enabling the exploration of their philosophical or theoretical commitments associated with the nature of logical connectives.</p>