 This abstract approach has led to generalized quantifier theory, see Barwise and Cooper 1981 as well as Peters and Westerståhl 2006. Among the most popular achievements of generalized quantifier theory is a semantic characterization of so-called ‘negative polarity items’: words like yet and ever. Their occurrence can be licensed by negation: The 6:05 has arrived yet is out, whereas The 6:05 hasn’t arrived yet is OK. But there are more contexts in which negative polarity items may occur, and syntacticians did not succeed in characterizing them. Ladusaw (1980) did so by using a characterization from generalized quantifier theory. This has been widely acknowledged as a great success for formal semantics. His proposal roughly was as follows. Downward entailing expressions are expressions that license inferences from supersets to subsets. No is downward entailing because from No man walks it follows that No father walks. A negative polarity item is acceptable only if it is interpreted in the scope of a downward entailing expression, e.g. No man ever walks. Further research showed that the analysis needed refining, and that a hierarchy of negative polarity items should be used (Ladusaw 1996, Homer 2021).