Szabolcsi (2004): Positive Polarity – Negative Polarity

Szabolcsi observes that someone cannot take scope immediately below clausemate negation, a negative quantifier or without, but can below at most five, and that what sets the first three apart is that they are anti-additive while at most five is merely decreasing. With someone's Fragment entry, which is blocked by anti-additive operators, the licensing theory blocks exactly the starred narrow-scope readings of her paradigm (readings_predicted), and over the paradigm's operators being blocked is being anti-additive (antiLicenses_someone_iff).

References

• [Sza04]

inductive Szabolcsi2004.Operator : Type

The operators of the paradigm, clausemate negation, no one, without and at most five.

• not : Operator
• noOne : Operator
• without : Operator
• atMostFive : Operator

@[instance_reducible]

instance Szabolcsi2004.instDecidableEqOperator : DecidableEq Operator

Equations

• Szabolcsi2004.instDecidableEqOperator x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Szabolcsi2004.instReprOperator.repr : Operator → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance Szabolcsi2004.instReprOperator : Repr Operator

Equations

• Szabolcsi2004.instReprOperator = { reprPrec := Szabolcsi2004.instReprOperator.repr }

def Szabolcsi2004.Operator.toLicensingContext : Operator → PolarityItem.LicensingContext

The licensing context an operator is.

Equations

• Szabolcsi2004.Operator.not.toLicensingContext = PolarityItem.LicensingContext.negation
• Szabolcsi2004.Operator.noOne.toLicensingContext = PolarityItem.LicensingContext.nobody
• Szabolcsi2004.Operator.without.toLicensingContext = PolarityItem.LicensingContext.withoutClause
• Szabolcsi2004.Operator.atMostFive.toLicensingContext = PolarityItem.LicensingContext.atMost

theorem Szabolcsi2004.antiLicenses_someone_iff (op : Operator) : op.toLicensingContext.licenser.AntiLicenses English.PolarityItems.someone ↔ op.toLicensingContext.licenser.Holds NaturalLogic.Signature.antiAdd

Someone is blocked immediately below an operator of the paradigm exactly when the operator is anti-additive.

def Szabolcsi2004.Operator.ofKey : String → Option Operator

The operator a row names.

Equations

• Szabolcsi2004.Operator.ofKey "not" = some Szabolcsi2004.Operator.not
• Szabolcsi2004.Operator.ofKey "no one" = some Szabolcsi2004.Operator.noOne
• Szabolcsi2004.Operator.ofKey "without" = some Szabolcsi2004.Operator.without
• Szabolcsi2004.Operator.ofKey "at most five" = some Szabolcsi2004.Operator.atMostFive
• Szabolcsi2004.Operator.ofKey x✝ = none

theorem Szabolcsi2004.readings_predicted (d : Datum) : d ∈ Examples.all → d.feature? "item" = some "someone" ∧ ∃ op ∈ (d.feature? "operator").bind Operator.ofKey, ∃ r ∈ d.readings.head?, r.2 = Judgment.acceptable ↔ ¬op.toLicensingContext.licenser.AntiLicenses English.PolarityItems.someone

Every row is on someone, names its operator, and its reading with someone in the operator's immediate scope is acceptable exactly when the operator does not block someone.