Negation and Generalized Quantifiers

Linguistic research has clearly shown that natural languages exhibit different forms of negation. Foremost among these are sentence negation and predicate negation. In this study, the relationship between both will be discussed. In particular, it wiu be argued that we can give an accurate description of the logical connections between sentence negation and predicate negation by reference to the semantical nature of the subject noun phrase. To this end, two important classes of generalized quantifiers will be distinguished, having to do with the familiar logical notions of consistency and completeness. Next, it will be shown that the distribution of negative adverbs in languages as Dutch and German forces us to make a distinction between predicate negation and verb negation as well. The logical relationship between these two forms of negation appears to be the same as that between sentence negation and predicate negation. Finally, it will be demonstrated that the difference between predicate negation and verb negation also shows up in languages such as English, particularly in co~ec t ion with monotonicity patterns.