  Now the more technical part begins. There are two kinds of variables, object variables as before, and intension variables, or individual concept variables, \(f, g, g_{1}, g_{2},\ldots\). With two kinds of variables present, the formation of atomic formulas becomes a little more complex. From now on, instead of just being \(n\)-place for some \(n\), a relation symbol will have a type associated with it, where a type is an \(n\)-tuple whose entries are members of \(\{O, I\}\). An atomic formula is an expression of the form \(P(\alpha_{1}, \ldots ,\alpha_{n})\) where \(P\) is a relation symbol whose type is \(\langle t_{1}, \ldots ,t_{n}\rangle\) and, for each \(i\), if \(t_{i} = O\) then \(\alpha_{i}\) is an object variable, and if \(t_{i} = I\) then \(\alpha_{i}\) is an intension variable. Among the relation symbols we still have \(E\), which now is of type \(\langle O\rangle\), and we have \(=\), of type \(\langle O,O \rangle\).