A research that takes Henkin's ideas in this direction is that of María Manzano, one of his students, whose proposal is to use Many-Sorted Logic as a common framework for the translation of logics. The aims of this proposal can be synthesized into two: 1) to use a single deductive calculus for all of them; and 2) to use the metaproperties of Many-Sorted Logic in order to more easily proof metaproperties of other logics. In addition, having a logical framework is useful for comparing different logics by comparing the theories that represent them. Although Henkin does not speak of formulae translation, nor does he make explicit a Many-Sorted Language or calculus, the ideas he uses in two of his articles serve as a basis for the approach to translation:Manzano, María (2014). «April the 19th.». In Manzano et al., ed. The Life and Work of Leon Henkin, Essays on His Contributions (en inglés). Springer International Publishing. . doi:10.1007/978-3-319-09719-0_11. "Completeness in the theory of types" and "Banishing the Rule of Substitution for Functional Variables".
