Conversely, an upward-entailing operator constrains the meaning of an expression to a higher number or degree, for example "more than one."
Ladusaw (1980) proposed that downward entailment is the property that licenses polarity items.
Subsequent attempts to describe the behavior of polarity items rely on a broader notion of nonveridicality.
Giannakidou (2002) argues that Strawson-DE allows not just the presupposition of the evaluated sentence but just any arbitrary proposition to count as relevant.
This results in over-generalization that validates the use if any in contexts where it is, in fact, ungrammatical, such as clefts, preposed exhaustive focus, and each/both: