 Alphabet: The alphabet of a many-sorted language \(L\) includes all the relation, function, and constant symbols in a set called \(\OperSym\), as well as an infinite number of variables for each sort \(s_{i}\in \Sort\), and the corresponding sets of variables are disjoint. An n-ary relation symbol \(R\) could be strict or liberal and, in the first case, we must provide information about what are the involved sorts. To achieve this requirement, we define a function \(\Rank\) having as domain the set \(\OperSym\) and whose values are either natural numbers other than zero (liberal option) or finite strings of \(\Sort\cup \{ 0\}\) (strict option). For any strict \(f\in \OperSym\), its value \(\Rank(f)\) always has the form \(\langle i_{1},\ldots,i_{m},i_{0}\rangle\), with \(i_{0},i_{1},\ldots,i_{m}\in \Sort\cup \{ 0\}\). When \(f\) is an m-ary predicate, \(i_{0}=0\), and \(i_{0}\not=0\) for m-ary function symbols; individual constants are considered as zero-ary function symbols with \(\Rank(f)=\langle i_{0}\rangle\), simplified as \(i_{0}\).