 In order to avoid unnecessary complications we will assume in the sequel that all the logics use the same denumerable set \(V\) of variables, so that the definition of formula of \(L\) depends only on \(L\). A logic system (or logic for short) is given by a language \(L\) and a consequence relation \(\vdash\) on the set of formulas of \(L\) that is formal in the sense that for every substitution \(\sigma\), every set of formulas \(\Gamma\) and every formula \(\phi\),