Three levels of translation into many-sorted logic Mar´ ıa Manzano & Julio Ostal´ e {mara,ostale}@usal.es University of Salamanca (Spain) Abstract We assume the opinion by which “tranlation into classical logic” is a reliable methodology of Universal Logic in the task of comparing differ- ent logics. What we add in this paper, following Manzano [9], is some evidence for adopting the slightly different paradigm of “tranlation into many-sorted classical logic.” Our own methodology, splitted into three levels of translation, is discussed in some detail. 1 Translation: a paradigm for Universal Logic 1.1 Some contextualization Universal Logic, according to B´ eziau [2], is the general theory of logical struc- tures. In other words: it plays in logic the same role that Universal Algebra does in algebra. Universal Logic is admittedly not a new logic; it contributes, however, to unify already existing logics. Its research program has been around for many years. Think that, in a sense, the approach of Universal Logic is as old as the reflections on what is classical logic, what is a connective, what is a deviant logic, how can we transfer metaproperties from one logic to another, how can we create a new logic with such-and-such features, etc. To take an example: the philosophical question “what counts as a logical inference” has led, from the pioneer papers of Tarski, Gentzen and Scott through the compilation of Gabbay [4], to several formal answers. These answers, in turn, are closely related to different methodologies that focus on the way certain metatheorems apply to some (but perhaps not every) logic. If you grasp logical inference from a proof-theoretical point of view, your style of comparing logics will rest upon morphisms between calculi; likewise, if you see the problem from a model-theoretical perspective, you will presumably compare logics by defining morphisms between the structures those logics try to describe. In either case, morphisms between languages have to be considered as well. Of course things are more complicate than sketched above. We should rather say that some methodologies are proof-oriented, others are model-oriented, and finally some others are conceived in purely abstract terms, inspired e.g. by the Tarskian consequence operator. This is the landscape: 1