structure Phenomena.Polarity.DisjunctionIgnorance.DisjunctionIgnoranceDatum : Type

Empirical pattern: Disjunction and speaker ignorance.

"Harry is in Antwerp or Brussels" implicates:

1. Speaker doesn't know Harry is in Antwerp
2. Speaker doesn't know Harry is in Brussels

Source: @cite{gazdar-1979}, @cite{geurts-2010} Ch. 3.3

• disjunction : String

  The disjunctive statement

• disjunctA : String

  First disjunct

• disjunctB : String

  Second disjunct

• inferenceA : String

  Ignorance inference about A

• inferenceB : String

  Ignorance inference about B

def Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionIgnoranceDatum.repr : DisjunctionIgnoranceDatum → ℕ → Std.Format

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instance Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionIgnoranceDatum : Repr DisjunctionIgnoranceDatum

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• Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionIgnoranceDatum = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionIgnoranceDatum.repr }

def Phenomena.Polarity.DisjunctionIgnorance.harryLocation : DisjunctionIgnoranceDatum

Classic example: Harry's location. Source: @cite{geurts-2010} p.61

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def Phenomena.Polarity.DisjunctionIgnorance.maryLocation : DisjunctionIgnoranceDatum

Location example with Mary.

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def Phenomena.Polarity.DisjunctionIgnorance.johnActivity : DisjunctionIgnoranceDatum

Activity example.

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def Phenomena.Polarity.DisjunctionIgnorance.disjunctionIgnoranceExamples : List DisjunctionIgnoranceDatum

All basic ignorance examples.

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structure Phenomena.Polarity.DisjunctionIgnorance.IgnoranceVsScalarDatum : Type

Comparison between ignorance and scalar implicatures.

Scalar implicatures and ignorance inferences differ:

• Scalar: speaker knows the stronger alternative is false
• Ignorance: speaker doesn't know which disjunct is true

• utterance : String

  The utterance

• inferenceType : String

  Type of inference

• inference : String

  The inference

• speakerClaimsKnowledge : Bool

  Is speaker claiming knowledge?

instance Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceVsScalarDatum : Repr IgnoranceVsScalarDatum

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• Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceVsScalarDatum = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceVsScalarDatum.repr }

def Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceVsScalarDatum.repr : IgnoranceVsScalarDatum → ℕ → Std.Format

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def Phenomena.Polarity.DisjunctionIgnorance.someScalar : IgnoranceVsScalarDatum

"Some" triggers scalar implicature (speaker knows).

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def Phenomena.Polarity.DisjunctionIgnorance.orIgnorance : IgnoranceVsScalarDatum

"Or" triggers ignorance (speaker doesn't know).

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def Phenomena.Polarity.DisjunctionIgnorance.comparisonExamples : List IgnoranceVsScalarDatum

All comparison examples.

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• Phenomena.Polarity.DisjunctionIgnorance.comparisonExamples = [Phenomena.Polarity.DisjunctionIgnorance.someScalar, Phenomena.Polarity.DisjunctionIgnorance.orIgnorance]

structure Phenomena.Polarity.DisjunctionIgnorance.LongDisjunctionIgnoranceDatum : Type

Ignorance extends to long disjunctions (n > 2).

For "A or B or C", we get ignorance about each disjunct:

• Speaker doesn't know A
• Speaker doesn't know B
• Speaker doesn't know C

Source: @cite{geurts-2010} p.61-64

• disjunction : String

  The disjunctive statement

• disjuncts : List String

  List of disjuncts

• ignoranceInferences : List String

  Ignorance inferences (one per disjunct)

instance Phenomena.Polarity.DisjunctionIgnorance.instReprLongDisjunctionIgnoranceDatum : Repr LongDisjunctionIgnoranceDatum

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• Phenomena.Polarity.DisjunctionIgnorance.instReprLongDisjunctionIgnoranceDatum = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprLongDisjunctionIgnoranceDatum.repr }

def Phenomena.Polarity.DisjunctionIgnorance.instReprLongDisjunctionIgnoranceDatum.repr : LongDisjunctionIgnoranceDatum → ℕ → Std.Format

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def Phenomena.Polarity.DisjunctionIgnorance.threeWayLocation : LongDisjunctionIgnoranceDatum

Three-way disjunction example. Source: @cite{geurts-2010} p.61

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def Phenomena.Polarity.DisjunctionIgnorance.fourWayActivity : LongDisjunctionIgnoranceDatum

Four-way disjunction example.

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def Phenomena.Polarity.DisjunctionIgnorance.longDisjunctionExamples : List LongDisjunctionIgnoranceDatum

All long disjunction examples.

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• Phenomena.Polarity.DisjunctionIgnorance.longDisjunctionExamples = [Phenomena.Polarity.DisjunctionIgnorance.threeWayLocation, Phenomena.Polarity.DisjunctionIgnorance.fourWayActivity]

structure Phenomena.Polarity.DisjunctionIgnorance.IgnoranceBlockingDatum : Type

Cases where ignorance inference is blocked or cancelled.

• context : String

  The context or construction

• sentence : String

  Example sentence

• ignoranceBlocked : Bool

  Is ignorance blocked?

• explanation : String

  Explanation

instance Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceBlockingDatum : Repr IgnoranceBlockingDatum

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• Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceBlockingDatum = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceBlockingDatum.repr }

def Phenomena.Polarity.DisjunctionIgnorance.instReprIgnoranceBlockingDatum.repr : IgnoranceBlockingDatum → ℕ → Std.Format

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def Phenomena.Polarity.DisjunctionIgnorance.explicitKnowledge : IgnoranceBlockingDatum

Explicit knowledge blocks ignorance.

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def Phenomena.Polarity.DisjunctionIgnorance.rhetoricalQuestion : IgnoranceBlockingDatum

Rhetorical questions don't trigger ignorance.

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def Phenomena.Polarity.DisjunctionIgnorance.embeddedBelief : IgnoranceBlockingDatum

Embedded disjunction under belief.

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def Phenomena.Polarity.DisjunctionIgnorance.blockingExamples : List IgnoranceBlockingDatum

All blocking examples.

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structure Phenomena.Polarity.DisjunctionIgnorance.QuantifiedIgnoranceDatum : Type

Interaction between disjunction ignorance and quantifiers.

• sentence : String

  The sentence

• quantifierScope : String

  Quantifier scope

• inference : String

  Ignorance inference

• notes : String

  Notes on the reading

instance Phenomena.Polarity.DisjunctionIgnorance.instReprQuantifiedIgnoranceDatum : Repr QuantifiedIgnoranceDatum

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• Phenomena.Polarity.DisjunctionIgnorance.instReprQuantifiedIgnoranceDatum = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprQuantifiedIgnoranceDatum.repr }

def Phenomena.Polarity.DisjunctionIgnorance.instReprQuantifiedIgnoranceDatum.repr : QuantifiedIgnoranceDatum → ℕ → Std.Format

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def Phenomena.Polarity.DisjunctionIgnorance.universalScopeDisj : QuantifiedIgnoranceDatum

Disjunction in scope of universal.

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def Phenomena.Polarity.DisjunctionIgnorance.disjScopeUniversal : QuantifiedIgnoranceDatum

Disjunction scoping over universal.

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def Phenomena.Polarity.DisjunctionIgnorance.quantifiedIgnoranceExamples : List QuantifiedIgnoranceDatum

All quantified ignorance examples.

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• Phenomena.Polarity.DisjunctionIgnorance.quantifiedIgnoranceExamples = [Phenomena.Polarity.DisjunctionIgnorance.universalScopeDisj, Phenomena.Polarity.DisjunctionIgnorance.disjScopeUniversal]

Positional Asymmetry in Disjunction Interpretation

@cite{chierchia-2013} "Logic in Grammar" Ch.1 observes that the same lexical material yields different preferred readings based on structural position:

Position	Polarity	Preferred Reading
Consequent of conditional	UE	Exclusive
Antecedent of conditional	DE	Inclusive
Scope of "every"	UE	Exclusive
Restrictor of "every"	DE	Inclusive
Positive sentence	UE	Exclusive
Negative sentence	DE	Inclusive

The Core Pattern

UE contexts: exclusive reading preferred

• "If everything goes well, we'll hire Mary or Sue"
• Default: we'll hire exactly one of them

DE contexts: inclusive reading preferred

• "If we hire Mary or Sue, everything will go well"
• Default: hiring either or both leads to success

Explanation via Maximize Strength

The asymmetry follows from the Maximize Strength principle:

• In UE: adding "not both" strengthens → compute SI
• In DE: adding "not both" would weaken → don't compute SI

When the exclusive SI is not computed, the inclusive reading emerges.

inductive Phenomena.Polarity.DisjunctionIgnorance.DisjunctionReading : Type

Type of disjunction interpretation.

• inclusive : DisjunctionReading
• exclusive : DisjunctionReading

instance Phenomena.Polarity.DisjunctionIgnorance.instDecidableEqDisjunctionReading : DecidableEq DisjunctionReading

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• Phenomena.Polarity.DisjunctionIgnorance.instDecidableEqDisjunctionReading x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionReading : BEq DisjunctionReading

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• Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionReading = { beq := Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionReading.beq }

def Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionReading.beq : DisjunctionReading → DisjunctionReading → Bool

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• Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionReading.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionReading : Repr DisjunctionReading

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• Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionReading = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionReading.repr }

def Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionReading.repr : DisjunctionReading → ℕ → Std.Format

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inductive Phenomena.Polarity.DisjunctionIgnorance.DisjunctionPosition : Type

Structural position of the disjunction.

• matrix : DisjunctionPosition
• conditional_cons : DisjunctionPosition
• conditional_ant : DisjunctionPosition
• every_scope : DisjunctionPosition
• every_restrictor : DisjunctionPosition
• negation_scope : DisjunctionPosition

instance Phenomena.Polarity.DisjunctionIgnorance.instDecidableEqDisjunctionPosition : DecidableEq DisjunctionPosition

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• Phenomena.Polarity.DisjunctionIgnorance.instDecidableEqDisjunctionPosition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionPosition.beq : DisjunctionPosition → DisjunctionPosition → Bool

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• Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionPosition.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionPosition : BEq DisjunctionPosition

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• Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionPosition = { beq := Phenomena.Polarity.DisjunctionIgnorance.instBEqDisjunctionPosition.beq }

def Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionPosition.repr : DisjunctionPosition → ℕ → Std.Format

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instance Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionPosition : Repr DisjunctionPosition

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• Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionPosition = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprDisjunctionPosition.repr }

def Phenomena.Polarity.DisjunctionIgnorance.positionPolarity : DisjunctionPosition → Core.NaturalLogic.ContextPolarity

Determine context polarity from position.

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• Phenomena.Polarity.DisjunctionIgnorance.positionPolarity Phenomena.Polarity.DisjunctionIgnorance.DisjunctionPosition.matrix = Core.NaturalLogic.ContextPolarity.upward
• Phenomena.Polarity.DisjunctionIgnorance.positionPolarity Phenomena.Polarity.DisjunctionIgnorance.DisjunctionPosition.conditional_cons = Core.NaturalLogic.ContextPolarity.upward
• Phenomena.Polarity.DisjunctionIgnorance.positionPolarity Phenomena.Polarity.DisjunctionIgnorance.DisjunctionPosition.conditional_ant = Core.NaturalLogic.ContextPolarity.downward
• Phenomena.Polarity.DisjunctionIgnorance.positionPolarity Phenomena.Polarity.DisjunctionIgnorance.DisjunctionPosition.every_scope = Core.NaturalLogic.ContextPolarity.upward
• Phenomena.Polarity.DisjunctionIgnorance.positionPolarity Phenomena.Polarity.DisjunctionIgnorance.DisjunctionPosition.every_restrictor = Core.NaturalLogic.ContextPolarity.downward
• Phenomena.Polarity.DisjunctionIgnorance.positionPolarity Phenomena.Polarity.DisjunctionIgnorance.DisjunctionPosition.negation_scope = Core.NaturalLogic.ContextPolarity.downward

def Phenomena.Polarity.DisjunctionIgnorance.predictReading : Core.NaturalLogic.ContextPolarity → DisjunctionReading

Predict preferred reading from polarity. UE → exclusive (SI computed), DE → inclusive (SI not computed). NM → inclusive (no clear strength ordering, so no exclusive SI).

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• Phenomena.Polarity.DisjunctionIgnorance.predictReading Core.NaturalLogic.ContextPolarity.upward = Phenomena.Polarity.DisjunctionIgnorance.DisjunctionReading.exclusive
• Phenomena.Polarity.DisjunctionIgnorance.predictReading Core.NaturalLogic.ContextPolarity.downward = Phenomena.Polarity.DisjunctionIgnorance.DisjunctionReading.inclusive
• Phenomena.Polarity.DisjunctionIgnorance.predictReading Core.NaturalLogic.ContextPolarity.nonMonotonic = Phenomena.Polarity.DisjunctionIgnorance.DisjunctionReading.inclusive

structure Phenomena.Polarity.DisjunctionIgnorance.ExclusiveInclusiveExample : Type

Example showing exclusive/inclusive asymmetry.

• sentence : String

  The sentence

• position : DisjunctionPosition

  Position of disjunction

• polarity : Core.NaturalLogic.ContextPolarity

  Polarity of that position

• preferredReading : DisjunctionReading

  Preferred reading

• canForceOther : Bool

  Can the other reading be forced with context?

• source : String

  Source

def Phenomena.Polarity.DisjunctionIgnorance.instReprExclusiveInclusiveExample.repr : ExclusiveInclusiveExample → ℕ → Std.Format

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instance Phenomena.Polarity.DisjunctionIgnorance.instReprExclusiveInclusiveExample : Repr ExclusiveInclusiveExample

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• Phenomena.Polarity.DisjunctionIgnorance.instReprExclusiveInclusiveExample = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprExclusiveInclusiveExample.repr }

def Phenomena.Polarity.DisjunctionIgnorance.hiring_consequent : ExclusiveInclusiveExample

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def Phenomena.Polarity.DisjunctionIgnorance.hiring_antecedent : ExclusiveInclusiveExample

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def Phenomena.Polarity.DisjunctionIgnorance.matrix_exclusive : ExclusiveInclusiveExample

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def Phenomena.Polarity.DisjunctionIgnorance.every_scope : ExclusiveInclusiveExample

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def Phenomena.Polarity.DisjunctionIgnorance.every_restrictor : ExclusiveInclusiveExample

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def Phenomena.Polarity.DisjunctionIgnorance.negation_scope : ExclusiveInclusiveExample

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def Phenomena.Polarity.DisjunctionIgnorance.exclusiveInclusiveExamples : List ExclusiveInclusiveExample

All exclusive/inclusive examples.

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Forcing Non-Preferred Readings

While polarity determines the default reading, context can force the non-preferred interpretation:

Forcing Inclusive in UE (harder)

"If everything goes well, we'll hire Mary or Sue, or both."

• Explicit "or both" forces inclusive

Forcing Exclusive in DE (harder)

"If we hire Mary or Sue but not both, everything will go well."

• Explicit "but not both" forces exclusive

The observation: forcing requires explicit marking. The unmarked reading follows from Maximize Strength.

structure Phenomena.Polarity.DisjunctionIgnorance.ForcedReadingExample : Type

Example of forcing a non-preferred reading.

• baseSentence : String

  The base sentence

• position : DisjunctionPosition

  Position (determines default)

• defaultReading : DisjunctionReading

  Default reading

• forcingPhrase : String

  Forcing phrase

• forcedReading : DisjunctionReading

  Resulting reading

• notes : String

  Notes

instance Phenomena.Polarity.DisjunctionIgnorance.instReprForcedReadingExample : Repr ForcedReadingExample

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• Phenomena.Polarity.DisjunctionIgnorance.instReprForcedReadingExample = { reprPrec := Phenomena.Polarity.DisjunctionIgnorance.instReprForcedReadingExample.repr }

def Phenomena.Polarity.DisjunctionIgnorance.instReprForcedReadingExample.repr : ForcedReadingExample → ℕ → Std.Format

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def Phenomena.Polarity.DisjunctionIgnorance.force_inclusive_ue : ForcedReadingExample

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def Phenomena.Polarity.DisjunctionIgnorance.force_exclusive_de : ForcedReadingExample

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def Phenomena.Polarity.DisjunctionIgnorance.forcedReadingExamples : List ForcedReadingExample

All forced reading examples.

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• Phenomena.Polarity.DisjunctionIgnorance.forcedReadingExamples = [Phenomena.Polarity.DisjunctionIgnorance.force_inclusive_ue, Phenomena.Polarity.DisjunctionIgnorance.force_exclusive_de]