 The notion of PTS was originally defined as an attempt to endow certain logics with recursive and palatable semantic interpretations. Actually, several paraconsistent logics which are not characterizable by finite matrices can be characterized by suitable combinations of many-valued logics. The idea of the decomposition is quite natural: given a logic \({{\cal L}}\), presented as a pair \({{\cal L}}=\langle C,\vdash_{{\cal L}}\rangle\) in which \(C\) is a signature and \(\vdash_{{\cal L}}\) is a consequence relation, a family of translations \(f_i:L(C) \to L(C_i)\) (for \(i\in I\)) is taken into consideration. Here, \(L(C)\) and \(L(C_i)\) denote the algebra of formulas defined by the signature \(C\) and \(C_i\), respectively. Recall that a translation from a logic \({{\cal L}}\) into a logic \({{\cal L}}'\) is a mapping \(f\) between the respective sets of formulas which preserve derivability, that is: \(\Gamma \vdash_{{\cal L}}\varphi\) (in the source logic \({{\cal L}}\)) implies that \(f(\Gamma) \vdash_{{{\cal L}}'} f(\varphi)\) (in the target logic \({{\cal L}}'\)).