Polarity item

In linguistics, a polarity item is a lexical item that can appear only in environments associated with a particular grammatical polarity – affirmative or negative. A polarity item that appears in affirmative (positive) contexts is called a positive polarity item (PPI), and one that appears in negative contexts is a negative polarity item (NPI) (redundantly: (negative) NPI item).
The environment in which a polarity item is permitted to appear is called a "licensing context". In the simplest case, an affirmative statement provides a licensing context for a PPI, while negation provides a licensing context for an NPI. However, there are many complications, and not all polarity items of a given type need necessarily have exactly the same set of licensing contexts.
In English.
As examples of polarity items, consider the English lexical items "somewhat" and "at all", as used in the following sentences:
As can be seen, "somewhat" is licensed by the affirmative environment of sentence (1), but it is forbidden (anti-licensed) by the negative environment of sentence (4). It can therefore be considered to be a positive polarity item (PPI). On the other hand, "at all" is licensed by the negative environment of sentence (2), but anti-licensed by the positive environment of sentence (3), and is therefore considered a negative polarity item (NPI). 
Because standard English does not have negative concord, that is, double negatives are not used to intensify each other, the language makes frequent use of certain NPIs that correspond in meaning to negative items, and can be used in the environment of another negative. For example, "anywhere" is an NPI corresponding to the negative "nowhere", as used in the following sentences:
Note that the alternative form with the double negative, *"I was not going nowhere", is ungrammatical in the standard language, although such forms are used in some colloquial English, and parallel the constructions used in certain other languages which have negative concord. ("Anywhere", like most of the other NPIs listed below, is also used in other senses where it is not an NPI, as in "I would go anywhere with you".) Similar pairs of negatives and corresponding NPI are listed below.
See also , and .
Determination of licensing contexts.
The actual set of contexts that license particular polarity items is not as easily defined as a simple distinction between affirmative and negative sentences. Baker noted that double negation may provide an acceptable context for positive polarity items:
However, licensing contexts can take many forms besides simple negation/affirmation. To complicate matters, polarity items appear to be highly idiosyncratic, each with its own set of licensing contexts.
Early discussion of polarity items can be found in the work of Otto Jespersen and Edward Klima. Much of the research on polarity items has centered around the question of what creates a negative context. In the late 1970s, William Ladusaw (building on work by Gilles Fauconnier) discovered that most English NPIs are licensed in downward entailing environments. This is known as the Fauconnier–Ladusaw hypothesis. A downward entailing environment, however, is not a necessary condition for an NPI to be licensed—they may be licensed by some non-monotone (and thus not downward entailing) contexts, like "exactly N", as well. 
Nor is a downward entailing environment a sufficient condition for all negative polarity items, as first pointed out by Zwarts (1981) for Dutch "ook maar".
Licensing contexts across languages include the scope of n-words (negative particles, negative quantifiers), the antecedent of conditionals, questions, the restrictor of universal quantifiers, non-affirmative verbs (doubt), adversative predicates (be surprised), negative conjunctions (without), comparatives and superlatives, "too"-phrases, negative predicates (unlikely), some subjunctive complements, some disjunctions, imperatives, and others (finally, only). Given this wide range of mostly non-downward entailing environments, the Fauconnier-Ladusaw Hypothesis has gradually been replaced in favor of theories based on the notion of nonveridicality (proposed by Zwarts and Giannakidou).
Different NPIs may be licensed by different expressions. Thus, while the NPI "anything" is licensed by the downward entailing expression "at most two of the visitors", the idiomatic NPI "not lift a finger" (known as a "minimizer") is not licensed by the same expression.
While NPIs have been discovered in many languages, their distribution is subject to substantial cross-linguistic variation; this aspect of NPIs is currently the subject of ongoing research in cross-linguistic semantics.