Polarity item
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Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....

, a polarity item is a lexical element that can appear only in the environment of a certain "licensing context." Polarity items are defined as Negative Polarity Items (NPIs) or Positive Polarity items (PPIs). Simple negation creates a licensing context for most NPIs, while affirmative statements license most PPIs.

To illustrate, consider these sentences using NPIs at all or any.
I didn't like the film at all
*I liked the film at all
John doesn't have any potatoes
*John has any potatoes.


In both pairs, the NPIs are licensed by negation. To illustrate a PPI, consider the word somewhat in the following pair:
John liked it somewhat.
*John didn't like it somewhat.


Somewhat is licensed by the affirmative environment, but it is forbidden (anti-licensed) by the negative environment (Baker 1970) . Baker also noticed that double negation may provide an acceptable context for positive polarity items:
I can't believe you don't fancy her somewhat.


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
Otto Jespersen
Jens Otto Harry Jespersen or Otto Jespersen was a Danish linguist who specialized in the grammar of the English language.He was born in Randers in northern Jutland and attended Copenhagen University, earning degrees in English, French, and Latin...

 and Edward Klima
Edward Klima
Edward S. Klima was an eminent linguist who specialized in the study of sign languages. Klima's work was heavily influenced by Noam Chomsky's then-revolutionary theory of the biological basis of linguistics, and applied that analysis to sign languages.Klima, much of whose work was in collaboration...

. Much of the research on polarity items has centered around the question of what creates a negative context. In the late seventies, William Ladusaw (building on work by Gilles Fauconnier
Gilles Fauconnier
Gilles Fauconnier is a French linguist, researcher in cognitive science, and author, currently working in the U.S.. He is a professor at the University of California, San Diego in the Department of Cognitive Science....

) discovered that most English NPIs are licensed in downward entailing
Downward entailing
In linguistic semantics, a downward entailing expression is one that denotes a monotone decreasing function. A downward entailing expression reverses the relation of semantic strength among expressions. An expression like "run fast" is semantically stronger than the expression "run" since "run...

 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.
*Some people have ever been on the moon.
Exactly three people have ever been on the moon.

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
Frans Zwarts
Frans Zwarts was the rector magnificus of the University of Groningen and a linguist and professor in the Department of Dutch Language and Culture with a specialty in semantics...

 and Giannakidou).

Different NPIs may be licensed by different expressions. Thus, while the NPI anything is licensed by the downward entailing
Downward entailing
In linguistic semantics, a downward entailing expression is one that denotes a monotone decreasing function. A downward entailing expression reverses the relation of semantic strength among expressions. An expression like "run fast" is semantically stronger than the expression "run" since "run...

 expression at most two visitors, the idiom
Idiom
Idiom is an expression, word, or phrase that has a figurative meaning that is comprehended in regard to a common use of that expression that is separate from the literal meaning or definition of the words of which it is made...

atic NPI lift a finger (known as a 'minimizer') is not licensed by the same expression.
At most two of the visitors had seen anything.
*At most two of the visitors lifted a finger to help.


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.

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