We investigate the question of obtaining a binary semantics for many-valued logics, in the lines of the so-called "Suszko's Thesis". Taking into account the issue of separability of truth-values, we develop a general algorithmic method to transform any truth-functional finitely-valued semantics into a manageable form of (possibly) non-truth-functional binary semantics, conformant with a certain clausal specification, to which we call "dyadic semantics". We also hint at how a dyadic semantics directly induces a tableau decision procedure for the logic, and provide several application examples, covering Gödel, Lukasiewicz and Kleene logics, as well as some paraconsistent systems. This talk is on ongoing joint work with W.A. Carnielli, M.E. Coniglio and J. Marcos from GTAL, UniCamp, Brazil.