 Strong negation fails as a semantic operation. Let us write \([\phi]\) for the set of models of sentence \(\phi\). In the special case of \(\mathbf{FO}\), the strong negation \({\sim}\) clearly defines a semantic operation: whenever \(\chi\) and \(\theta\) are sentences such that \([\chi] = [\theta]\), we have \([{\sim}\chi] = [{\sim}\theta]\). Burgess (2003) observed that in the context of IF logic this property is lost in a very strong sense. In fact there are IF sentences \(\chi\) and \(\theta\) such that while \([\chi] = [\theta]\), the sets \([{\sim}\chi]\) and \([{\sim}\theta]\) are not only distinct but even disjoint. 