 The notion of compositionality can be refined by imposing constraints on the auxiliary semantic attributes. Sandu and Hintikka (2001: 60) suggested, by analogy with \(\mathbf{FO}\), that ‘satisfaction by a single variable assignment’ would be a natural auxiliary attribute in connection with \(\mathbf{IFL}\). By the result of Cameron and Hodges, no semantics for \(\mathbf{IFL}\) exists that would be compositional in this restricted sense.