In this talk we propose a formal study of non-deterministic semantics for non-algebraizable logical systems using the tools of universal algebra, model theory and category theory. Specifically, we intend to address some open questions proposed in recent works on non-deterministic semantics and non-deterministic algebraization of logical systems through the paradigms of swap structures and structures of Fidel, developed in the Center of Logic and Epistemology of Science (CLE) of the Institute of Philosophy and Human Sciences (IFCH) of the University State of Campinas (UNICAMP).

On this presentation of our progress so far we shall focus on the multitude of definitions in the subject of multialgebras and the advantages of some definitions over others, on the utility of algebras over powersets as encoders of information on multialgebras, and on interpretations of swap and twist structures as universal algebras.