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 formal conditions for relative expressiveness have various levels of stringency, some results on lifting some conditions to stricter ones are explored. Finally, a discussion on the properties of these formal conditions is presented. Special attention is given to notion of meaning equivalence, and how one may consider that it holds or not, depending on the weight attributed to logical and non-logical constants in expressiveness comparisons.