 In clause 1 of the above definition we follow the common practice of giving a set-theoretical interpretation to the predication \(X(t_1,\ldots,t_n)\). Having interpreted X as a subset of \(M^n\), we interpret predication \(X(t_1,\ldots,t_n)\) as membership \((t^\mm_1 \langle s\rangle,\ldots,t^\mm_n \langle s\rangle) \in s(X)\). In clause 2 we interpret quantification over properties and relations as quantification over subsets of the cartesian product \(M^n\). Respectively, in clause 3 we interpret quantification over functions as quantification over sets that are functions \(M^n\to M\) in the set-theoretical sense.