Polarity items

A polarity item is a lexical item with a defective distribution: a negative polarity item occurs only in a negative context and a positive polarity item cannot occur in one ([vdW97]). Both are graded by the strength of negation of DEStrength ([Zwa98]): a negative polarity item needs at least some strength, which licenses it, and a positive polarity item is blocked by at least some strength, which anti-licenses it. The two are independent, and an item with both, like Dutch ooit 'ever', is bipolar. A free choice item is licensed in the generic contexts instead ([KL93], [Day96]); English any is both a negative polarity item and a free choice item.

The record also holds the contexts in which the item is attested and those in which it is attested to be out, the data against which Semantics/Polarity/Licensing.lean checks the theory.

Main declarations

• PolarityItem: the lexical record.
• PolarityItem.IsNPI, PolarityItem.IsPPI, PolarityItem.IsFCI: the classes.

References

• [Zwa98]
• [vdW97]
• [KL93]
• [Day96]

structure PolarityItem : Type

A polarity-sensitive lexical item: its form, the weakest strength of negation that licenses it and the weakest that blocks it, whether the generic contexts license it, and the contexts in which it is attested and attested to be out.

• form : String

  The surface form.

• licensor : Option DEStrength

  The weakest strength of negation that licenses the item, if it is a negative polarity item. A negative concord item that needs clausemate negation carries antiMorphic, the strength of clausal negation alone.

• antiLicensor : Option DEStrength

  The weakest strength of negation that blocks the item, if it is a positive polarity item.

• freeChoice : Bool

  Whether the generic contexts license the item.

• licensingContexts : List LicensingContext

  The contexts in which the item is attested.

• excludedContexts : List LicensingContext

  The contexts in which the item is attested to be out.

@[reducible, inline]

abbrev PolarityItem.IsNPI (e : PolarityItem) : Prop

An item is a negative polarity item when some strength of negation licenses it.

Equations

• e.IsNPI = (e.licensor.isSome = true)

@[reducible, inline]

abbrev PolarityItem.IsPPI (e : PolarityItem) : Prop

An item is a positive polarity item when some strength of negation blocks it.

Equations

• e.IsPPI = (e.antiLicensor.isSome = true)

@[reducible, inline]

abbrev PolarityItem.IsFCI (e : PolarityItem) : Prop

An item is a free choice item when the generic contexts license it.

Equations

• e.IsFCI = (e.freeChoice = true)