Title: Translations: generalizing relative expressiveness between logics,
Abstract: There is a strong demand for precise means for the comparison of logics in
terms of expressiveness both from theoretical and from application areas. The
aim of this paper is to propose a sufficiently general and reasonable formal
criterion for expressiveness, so as to apply not only to model-theoretic
logics, but also to Tarskian and proof-theoretic logics. For model-theoretic
logics there is a standard framework of relative expressiveness, based on the
capacity of characterizing structures, and a straightforward formal criterion
issuing from it. The problem is that it only allows the comparison of those
logics defined within the same class of models. The urge for a broader
framework of expressiveness is not new. Nevertheless, the enterprise is complex
and a reasonable model-theoretic formal criterion is still wanting. Recently
there appeared two criteria in this wider framework, one from García-Matos &
Väänänen and other from L. Kuijer. We argue that they are not adequate.
Their limitations are analyzed and we propose to move to an even broader
framework lacking model-theoretic notions, which we call "translational
expressiveness". There is already a criterion in this later framework by
Mossakowski et al., however it turned out to be too lax. We propose some
adequacy criteria for expressiveness and a formal criterion of translational
expressiveness complying with them is given.