 A propositional language (a language, for short) \(L\) is a set of connectives, that is, a set of symbols each one of which has an arity \(n\) that tells us in case that \(n = 0\) that the symbol is a propositional constant, and in case that \(n \gt 0\) whether the connective is unary, binary, ternary, etc. For example \(\{\wedge , \vee , \rightarrow , \bot , \top \}\) is (or can be) the language of several logics, like classical and intuitionistic, \((\bot\) and \(\top\) are 0-ary and the other connectives are binary), \(\{\neg , \wedge , \vee \rightarrow , \Box , \Diamond \}\) is the language of several modal logics, \((\neg , \Box , \Diamond\) are unary and the other connectives binary) and \(\{ \wedge , \vee , \rightarrow , * , \top , \bot , 1, 0\}\) is the language of many-valued logics and also of a fragment of linear logic \((\bot , \top , 1\), and 0 are propositional constants and the other symbols binary connectives).