Linglib.Phenomena.Polarity.NPIs

The Core type includes FC environments (modals, generics, imperatives);
the Phenomena type includes verbal licensors (doubt, deny) and finer-grained
negation (sentential vs constituent). The mappings below connect them.

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def Phenomena.Polarity.NPIs.LicensingContext.toCore :

LicensingContext → Option Core.Lexical.PolarityItem.LicensingContext

Map a Phenomena-level licensing context to its Core equivalent. Partial: universalRestrictor, doubtVerb, denyVerb have no Core counterpart.

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def Phenomena.Polarity.NPIs.LicensingContext.fromCore :

Core.Lexical.PolarityItem.LicensingContext → Option LicensingContext

Map a Core licensing context to its Phenomena equivalent. Partial: FC contexts (modals, generics, imperatives) and structural contexts (atMost, since_temporal, free_relative) have no Phenomena counterpart.

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theorem Phenomena.Polarity.NPIs.LicensingContext.fromCore_toCore (ctx : LicensingContext) (c : Core.Lexical.PolarityItem.LicensingContext) (h : ctx.toCore = some c) :

fromCore c = some ctx

Round-trip: when a Phenomena context maps to Core, mapping back recovers it.

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structure Phenomena.Polarity.NPIs.NPIDatum :

Type

An NPI licensing datum

sentence : String
The sentence
npiItem : String
The NPI item
grammatical : Bool
Grammaticality judgment (true = OK, false = bad)
context : Option LicensingContext
Type of licensing context (if grammatical)
notes : String
Notes

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The "Any" Paradigm #

@cite{israel-2011} @cite{kadmon-landman-1993} @cite{ladusaw-1979} @cite{lahiri-1998} @cite{van-rooy-2003}

"Any" is the classic English weak NPI. Licensed in DE contexts.

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def Phenomena.Polarity.NPIs.anyNegation :

NPIDatum

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def Phenomena.Polarity.NPIs.anyPositive :

NPIDatum

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Phenomena.Polarity.NPIs.anyPositive = { sentence := "*John saw anyone", npiItem := "anyone", grammatical := false, context := none, notes := "Positive (UE) context blocks NPI" }

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def Phenomena.Polarity.NPIs.anyQuestion :

NPIDatum

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def Phenomena.Polarity.NPIs.anyConditional :

NPIDatum

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def Phenomena.Polarity.NPIs.anyUniversal :

NPIDatum

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def Phenomena.Polarity.NPIs.anyOnly :

NPIDatum

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def Phenomena.Polarity.NPIs.anySuperlative :

NPIDatum

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def Phenomena.Polarity.NPIs.anyComparative :

NPIDatum

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def Phenomena.Polarity.NPIs.anyFew :

NPIDatum

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def Phenomena.Polarity.NPIs.anyWithout :

NPIDatum

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def Phenomena.Polarity.NPIs.anyBefore :

NPIDatum

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def Phenomena.Polarity.NPIs.anyToo :

NPIDatum

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def Phenomena.Polarity.NPIs.anyDoubt :

NPIDatum

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"Ever" - Temporal NPI #

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def Phenomena.Polarity.NPIs.everNegation :

NPIDatum

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def Phenomena.Polarity.NPIs.everPositive :

NPIDatum

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Phenomena.Polarity.NPIs.everPositive = { sentence := "*John has ever seen Paris", npiItem := "ever", grammatical := false, context := none, notes := "Positive context blocks \"ever\"" }

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def Phenomena.Polarity.NPIs.everQuestion :

NPIDatum

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def Phenomena.Polarity.NPIs.everConditional :

NPIDatum

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Strong NPIs #

Strong NPIs require ANTI-ADDITIVE contexts (not merely DE). "Few" and "at most 3" don't license them.

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def Phenomena.Polarity.NPIs.liftFingerNegation :

NPIDatum

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def Phenomena.Polarity.NPIs.liftFingerFew :

NPIDatum

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def Phenomena.Polarity.NPIs.liftFingerWithout :

NPIDatum

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def Phenomena.Polarity.NPIs.inYearsNegation :

NPIDatum

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def Phenomena.Polarity.NPIs.inYearsFew :

NPIDatum

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def Phenomena.Polarity.NPIs.inYearsQuestion :

NPIDatum

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"Yet" - Aspectual/Temporal Strong NPI #

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def Phenomena.Polarity.NPIs.yetNegation :

NPIDatum

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def Phenomena.Polarity.NPIs.yetQuestion :

NPIDatum

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def Phenomena.Polarity.NPIs.yetPositive :

NPIDatum

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Phenomena.Polarity.NPIs.yetPositive = { sentence := "*John has arrived yet", npiItem := "yet", grammatical := false, context := none, notes := "Positive context blocks \"yet\"" }

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"At All" - Scalar Endpoint NPI #

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def Phenomena.Polarity.NPIs.atAllNegation :

NPIDatum

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def Phenomena.Polarity.NPIs.atAllQuestion :

NPIDatum

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def Phenomena.Polarity.NPIs.atAllPositive :

NPIDatum

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Phenomena.Polarity.NPIs.atAllPositive = { sentence := "*John helped at all", npiItem := "at all", grammatical := false, context := none, notes := "Positive context blocks \"at all\"" }

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def Phenomena.Polarity.NPIs.atAllConditional :

NPIDatum

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Intervention Effects #

Some elements block NPI licensing even in DE contexts.

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def Phenomena.Polarity.NPIs.interventionQuantifier :

NPIDatum

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def Phenomena.Polarity.NPIs.noIntervention :

NPIDatum

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Free Choice "Any" #

Not the same as NPI "any"! Free choice any appears in modal/generic contexts.

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def Phenomena.Polarity.NPIs.fcAnyModal :

NPIDatum

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def Phenomena.Polarity.NPIs.fcAnyGeneric :

NPIDatum

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def Phenomena.Polarity.NPIs.fcAnyImperative :

NPIDatum

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Phenomena.Polarity.NPIs.fcAnyImperative = { sentence := "Take any card", npiItem := "any (FC)", grammatical := true, context := none, notes := "Free choice any in imperatives" }

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Cross-Linguistic Patterns #

NPIs exist in many languages with similar distribution.

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structure Phenomena.Polarity.NPIs.CrossLingNPI :

Type

Cross-linguistic NPI datum

language : String
npiItem : String
gloss : String
licensingContexts : List String
scalarDirection : Core.Lexical.PolarityItem.ScalarDirection
Scalar direction
notes : String

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def Phenomena.Polarity.NPIs.hindiKoii :

CrossLingNPI

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def Phenomena.Polarity.NPIs.greekKanenas :

CrossLingNPI

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def Phenomena.Polarity.NPIs.japaneseNanimo :

CrossLingNPI

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def Phenomena.Polarity.NPIs.germanJemals :

CrossLingNPI

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def Phenomena.Polarity.NPIs.germanSoRecht :

CrossLingNPI

German "so recht" — attenuating NPI. @cite{schwab-2022}: does NOT show NPI illusion.

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NPIs in Questions #

Key insight from van Rooy: NPIs in questions increase ENTROPY (average informativity). This makes questions more "general" and less biased.

Questions expecting negative answers → license NPIs
Questions expecting positive answers → license PPIs
Rhetorical questions → strong NPIs (lift a finger, etc.)

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structure Phenomena.Polarity.NPIs.NPIQuestionDatum :

Type

NPI in question datum

sentence : String
npiItem : String
questionType : String
grammatical : Bool
expectedBias : String
notes : String

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def Phenomena.Polarity.NPIs.everInQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.anyInPolarQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.anyInWhQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.anyInRestrictor :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.liftFingerQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.batAnEyeQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.aDropQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.millionYearsQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.ppiRatherQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.ppiPrettyQuestion :

NPIQuestionDatum

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def Phenomena.Polarity.NPIs.questionData :

List NPIQuestionDatum

All question data

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Minimizers vs Non-Minimizers #

@cite{israel-2001} notes NPIs like "all that" and "long" that don't denote minimal quantities. Their use under negation makes the sentence LESS informative, not more.

This challenges pure informativity-based accounts but supports relevance-based ones.

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def Phenomena.Polarity.NPIs.allThatNPI :

NPIDatum

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def Phenomena.Polarity.NPIs.longNPI :

NPIDatum

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def Phenomena.Polarity.NPIs.anyData :

List NPIDatum

All "any" examples

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def Phenomena.Polarity.NPIs.everData :

List NPIDatum

All "ever" examples

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Phenomena.Polarity.NPIs.everData = [Phenomena.Polarity.NPIs.everNegation , Phenomena.Polarity.NPIs.everPositive , Phenomena.Polarity.NPIs.everQuestion , Phenomena.Polarity.NPIs.everConditional ]

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def Phenomena.Polarity.NPIs.strongNPIData :

List NPIDatum

All strong NPI examples

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def Phenomena.Polarity.NPIs.yetData :

List NPIDatum

All "yet" examples

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Phenomena.Polarity.NPIs.yetData = [Phenomena.Polarity.NPIs.yetNegation , Phenomena.Polarity.NPIs.yetQuestion , Phenomena.Polarity.NPIs.yetPositive ]

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def Phenomena.Polarity.NPIs.atAllData :

List NPIDatum

All "at all" examples

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Core Empirical Generalizations #

1. The DE Generalization #

Weak NPIs are licensed in downward-entailing contexts.

Test: If "All As are Bs" entails "All As are Cs", then:

In UE contexts: "All As are Bs" entails "All As are Cs"
In DE contexts: "All As are Cs" entails "All As are Bs"

2. Anti-Additivity for Strong NPIs #

Strong NPIs require anti-additive contexts:

f(A∨B) = f(A) ∧ f(B)

"No one" is anti-additive: "No one saw A or B" = "No one saw A and no one saw B" "Few people" is merely DE: "Few saw A or B" ≠ "Few saw A and few saw B"

3. The Scalar Approach (Fauconnier, Krifka) #

NPIs involve scalar reversal:

In positive contexts: "some" > "any" (some is more informative)
In negative contexts: "any" > "some" (any is more informative)

4. Domain Widening #

"Any" widens the domain beyond contextual restriction:

"I don't have an opinion" (contextually restricted)
"I don't have any opinion" (widened to all opinions)

5. EVEN Theory #

NPIs involve covert EVEN:

[EVEN anyone] = "even the most unlikely person"
In DE contexts: wide domain = least likely = EVEN presupposition satisfied

6. Entropy/Utility #

NPIs maximize RELEVANCE (utility):

In assertions: strength = informativity (entailment)
In questions: strength = entropy (average informativity)
NPIs in questions increase entropy → more useful questions
Unifies assertion licensing (DE) with question licensing (bias reduction)

7. Local RSA Approach #

Local RSA derives NPI effects from polarity-sensitive informativity:

In UE: smaller domain = more informative = preferred (→ EXH effects)
In DE: wider domain = more informative = preferred (→ NPI licensing)
No covert EVEN needed - it's pragmatic inference

N-words and Scale-Minimality #

@cite{chierchia-2013} "Logic in Grammar" observes that N-WORDS (negative indefinites that participate in Negative Concord) are constrained to SCALE-MINIMAL elements.

What are N-words? #

N-words are negative indefinites in Romance/Slavic languages that:

Can appear in Negative Concord (NC) constructions
Have negative force when appearing alone
Lose negative force under c-commanding negation (NC)

Examples: Italian "nessuno" (no-one), "niente" (nothing), "neanche" (not even)

The Scale-Minimality Constraint #

N-words are formed ONLY from scale-minimal quantifiers:

Base	Scale Position	N-word?	Example
uno (one)	minimal	✓	nessuno
due (two)	non-minimal	✗	*nessdue
most	non-minimal	✗	*nessmost
every	maximal	✗	*nessevery

Why This Constraint? #

Chierchia's explanation via scalar implicature:

N-words require PURELY downward-entailing environments. But NON-MINIMAL scale positions generate POSITIVE implicatures:

"No more than ten" implicates "at least some" (positive component!)
This positive implicature DISRUPTS the DE environment
Only scale-MINIMAL elements avoid this problem

The "neanche" Test (Chierchia p.6-7) #

Italian "neanche" (roughly "not even N") shows this pattern clearly:

✓ "Non ho visto neanche un professore" (I didn't see even one professor)

✗ "*Non ho visto neanche due professori" (I didn't see even two professors)

BUT: "neanche due" becomes acceptable when "two" is contextually construed as MINIMAL on a relevant scale:

✓ "Quel problema non lo risolverebbero neanche due professori" (That problem wouldn't be solved by even two professors) [Context: two is the minimum expected number to solve it]

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inductive Phenomena.Polarity.NPIs.ScalePosition :

Type

Scale position of a quantifier/numeral.