On the Comparisons of Logics in Terms of Expressive Power

Abstract

This paper investigates the question "when is a logic more expressive than another?" In order to approach it, "logic" is understood in the model-theoretic sense and, contrary to other proposals in the literature, it is argued that relative expressiveness between logics is best framed with respect to the notion of expressing properties of models, a notion that can be captured precisely in various ways. It is shown that each precise rendering can give rise to a formal condition for relative expressiveness that has appeared in the literature. Five such conditions are exposed, tested for some properties and compared to each other. As the Manuscrito -Rev. Int. Fil. Campinas, v.46, n.4, e-2022-0054.R3.