We explore certain algebraic structures that naturally emerge within the framework of logics of synonymy, analytic containment, and hyperintensionality. In particular, we argue that Angell’s logic \(\textrm{AC}\) , one of the earliest and most successful attempts to analyse the properties of logical constants with a topic-transformative character, can be better understood through a direct algebraic study of De Morgan bisemilattices. Inter alia, we study and compare the quasivarieties of De Morgan bisemilattices generated by certain finite algebras considered in the literature, viewed as formalising different approaches to the validity of inferences among statements of synonymy.
