It is well known that the interpretation of sentences containing negated ‘neg-raising’ predicates like think and want give rise to surprisingly strong interpretations, which are interpreted the same way as when negation takes scope below the embedding predicate. For instance, James doesn’t think that Marie was promoted is generally interpreted in the same way as James thinks that Marie wasn’t promoted. Neg-raising has also been linked to the licensing of strong Negative Polarity Items (NPIs), a subclass of NPIs including e.g. in years, as in James doesn’t think that Marie has seen her mother in years. There are two main approaches to neg-raising in the literature. The first approach is syntactic, and holds that, in neg-raising sentences, negation, while appearing in the main clause at the level of surface structure, is assumed to actually be in the embedded clause at some syntactic level, in particular at the level that feeds into semantic interpretation. The second is a semantic/pragmatic approach, in which neg-raising arises as an inference due to an excluded middle presupposition or implicature of neg-raising predicates. In this squib, we present data involving attitude predicates like appreciate, be glad, be happy or like which both give rise to neg-raising interpretations and presuppose the truth of their sentential complements. We argue that accounting for the neg-raising interpretation of the negations of these predicates, and the fact that they fail to license strong NPIs, constitutes a challenge for existing semantic and syntactic approaches to neg-raising. We show that the semantic approach can, however, be easily amended to accommodate such cases, whereas the problem seems much deeper for syntactic approaches, furnishing a new argument for semantic approaches to neg-raising.