 So if \(\phi\) and \(\psi\) are \(\mathbf{IFL}\) formulas, e.g. \(\neg \phi\) and \((\neg \phi \vee \psi)\) are \(\mathbf{EIFL}\) formulas; by contrast \((\forall x)\neg \phi\) is not. For the crucial restriction that \(\neg\) may not occur in the scope of a quantifier, see Hintikka (1991: 49; 1996: 148). For counterexamples to this restriction see, however, Hintikka (1996: 148; 2002c) and especially Hintikka (2006b) in which the so-called fully extended IF first-order logic (FEIFL) is considered. In FEIFL, any occurrences of \(\neg\) are allowed which are subject to the following syntactic condition: if (Q\(x/W)\) is a quantifier in the syntactic scope of an occurrence of \(\neg\), then all quantifiers listed in \(W\) are likewise in the syntactic scope of that occurrence of \(\neg\).