  A first-order valuation in FOIL model   \(\cM\) is a mapping that assigns to each  object variable a member of \(\bD_{O}\), as before, and to each intension variable a member of \(\bD_{i}\). If \(f\) is an intension variable, we’ll write \(v(f, \Gamma )\) for \(v(f)(\Gamma )\). Now, the definition of truth, at a state \(\Gamma\) of a model  \(\cM\), with respect to a valuation  \(v\), meets the conditions set forth in Section 3.2.2 and, in addition, the following: