Disjunction Ignorance [Chi13] #
Empirical patterns for ignorance inferences from disjunction, organized around [Chi13]'s positional-asymmetry account.
"Harry is in Antwerp or Brussels" implicates:
- Speaker doesn't know Harry is in Antwerp
- Speaker doesn't know Harry is in Brussels
This is different from scalar implicature:
- Scalar: "some" → speaker knows not all
- Ignorance: "A or B" → speaker doesn't know which
The file provides a predictReading function over ContextPolarity
(from NaturalLogic) that derives the preferred inclusive/exclusive
reading from structural position.
Empirical pattern: Disjunction and speaker ignorance.
"Harry is in Antwerp or Brussels" implicates:
- Speaker doesn't know Harry is in Antwerp
- Speaker doesn't know Harry is in Brussels
Source: [Sta79], [Geu10] 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
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Classic example: Harry's location. Source: [Geu10] p.61
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Location example with Mary.
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Activity example.
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All basic ignorance examples.
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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?
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"Some" triggers scalar implicature (speaker knows).
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- Chierchia2013.someScalar = { utterance := "Some students passed", inferenceType := "scalar", inference := "Speaker believes not all students passed", speakerClaimsKnowledge := true }
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"Or" triggers ignorance (speaker doesn't know).
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- Chierchia2013.orIgnorance = { utterance := "John passed or Mary passed", inferenceType := "ignorance", inference := "Speaker doesn't know which one passed", speakerClaimsKnowledge := false }
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All comparison examples.
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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: [Geu10] p.61-64
- disjunction : String
The disjunctive statement
- disjuncts : List String
List of disjuncts
- ignoranceInferences : List String
Ignorance inferences (one per disjunct)
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Three-way disjunction example. Source: [Geu10] p.61
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Four-way disjunction example.
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All long disjunction examples.
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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
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Explicit knowledge blocks ignorance.
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Rhetorical questions don't trigger ignorance.
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Embedded disjunction under belief.
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All blocking examples.
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Interaction between disjunction ignorance and quantifiers.
- sentence : String
The sentence
- quantifierScope : String
Quantifier scope
- inference : String
Ignorance inference
- notes : String
Notes on the reading
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Disjunction in scope of universal.
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Disjunction scoping over universal.
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All quantified ignorance examples.
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Positional Asymmetry in Disjunction Interpretation #
[Chi13] "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.
Type of disjunction interpretation.
- inclusive : DisjunctionReading
- exclusive : DisjunctionReading
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- Chierchia2013.instDecidableEqDisjunctionReading x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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Structural position of the disjunction.
- matrix : DisjunctionPosition
- conditional_cons : DisjunctionPosition
- conditionalAntecedent : DisjunctionPosition
- every_scope : DisjunctionPosition
- every_restrictor : DisjunctionPosition
- negation_scope : DisjunctionPosition
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- Chierchia2013.instDecidableEqDisjunctionPosition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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Determine context polarity from position.
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- Chierchia2013.positionPolarity Chierchia2013.DisjunctionPosition.matrix = NaturalLogic.ContextPolarity.upward
- Chierchia2013.positionPolarity Chierchia2013.DisjunctionPosition.conditional_cons = NaturalLogic.ContextPolarity.upward
- Chierchia2013.positionPolarity Chierchia2013.DisjunctionPosition.conditionalAntecedent = NaturalLogic.ContextPolarity.downward
- Chierchia2013.positionPolarity Chierchia2013.DisjunctionPosition.every_scope = NaturalLogic.ContextPolarity.upward
- Chierchia2013.positionPolarity Chierchia2013.DisjunctionPosition.every_restrictor = NaturalLogic.ContextPolarity.downward
- Chierchia2013.positionPolarity Chierchia2013.DisjunctionPosition.negation_scope = NaturalLogic.ContextPolarity.downward
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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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- Chierchia2013.predictReading NaturalLogic.ContextPolarity.upward = Chierchia2013.DisjunctionReading.exclusive
- Chierchia2013.predictReading NaturalLogic.ContextPolarity.downward = Chierchia2013.DisjunctionReading.inclusive
- Chierchia2013.predictReading NaturalLogic.ContextPolarity.nonMonotonic = Chierchia2013.DisjunctionReading.inclusive
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Example showing exclusive/inclusive asymmetry.
- sentence : String
The sentence
- position : DisjunctionPosition
Position of disjunction
- polarity : NaturalLogic.ContextPolarity
Polarity of that position
- preferredReading : DisjunctionReading
Preferred reading
- canForceOther : Bool
Can the other reading be forced with context?
- source : String
Source
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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.
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
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All forced reading examples.
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Universal Free Choice Items #
Universal FCIs like English "any" and Italian "qualunque" contrast with existential FCIs (irgendein, yek-i, vreun) handled in [AOM25a]:
| FCI Type | Base Force | Examples | Morphological Hints |
|---|---|---|---|
| Existential | ∃ | irgendein, yek-i, vreun | Often contains "one" |
| Universal | ∀ | any, qualunque, whatever | Often wh-based |
Chierchia's analysis #
Both FCI types have the same underlying existential semantics. The universal force of "any" emerges from obligatory exhaustification of domain alternatives.
- "any" = ∃ + obligatory domain alternatives (always active)
- "some" = ∃ + optional domain alternatives (relevance-gated)
The "any" Distribution #
NPI use (DE contexts): "I didn't see any students"
- In DE, exhaustification is vacuous (domain alts are entailed)
- Result: plain existential reading
FC use (modal contexts): "You may read any book"
- Under modal, domain alts yield free choice
- Result: universal-like permission
Generic use: "Any owl hunts mice" (subtrigging)
- Generic contexts license FC reading
- Result: universal generalization
Why "any" Fails in Positive Episodic Contexts #
"*There are any cookies"
Exhaustifying domain alternatives in UE episodic contexts yields contradiction:
- ∃d∈D. P(d) (assertion)
- ∀d∈D. ¬[P(d) ∧ ∀y≠d.¬P(y)] (domain alt negation)
With two witnesses d₁, d₂: the second clause requires that for any d satisfying P, some other y also satisfies P. Combined with the first clause, this leads to infinite regress/contradiction for finite domains.
Contrast with "some" #
"Some" has the same alternatives as "any", but they are optional. When not activated (low relevance), "some" = plain existential. "Any" must activate alternatives, hence the restricted distribution.
Universal FCI: existential with obligatorily active domain alternatives.
- baseIsExistential : Bool
Base meaning is existential
- obligatoryDomainAlts : Bool
Domain alternatives are always active (not relevance-gated)
- modalRescue : Bool
Can be rescued via modal insertion
- genericRescue : Bool
Can be rescued via generic/subtrigging
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English "any" as a Universal FCI
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Italian "qualunque" as a Universal FCI
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Context type for determining Universal FCI distribution.
- positiveEpisodic : UFCIContext
- negation : UFCIContext
- conditionalAntecedent : UFCIContext
- deonticModal : UFCIContext
- epistemicModal : UFCIContext
- generic : UFCIContext
- question : UFCIContext
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- Chierchia2013.instDecidableEqUFCIContext x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Chierchia2013.instReprUFCIContext = { reprPrec := Chierchia2013.instReprUFCIContext.repr }
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Surface reading available to a Universal FCI.
Subset of the broader EFCI reading taxonomy: UFCIs only ever yield plain existential (NPI use, no exhaustification effect) or free choice (via modal/generic rescue). Uniqueness, modal variation, and epistemic ignorance are existential-FCI-specific readings.
- plainExistential : UFCIReading
Plain existential (NPI use in DE contexts)
- freeChoice : UFCIReading
Free choice (modal/generic rescue)
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- Chierchia2013.instDecidableEqUFCIReading x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Chierchia2013.instReprUFCIReading = { reprPrec := Chierchia2013.instReprUFCIReading.repr }
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FCI flavor: existential vs universal force.
Note: "Universal" FCIs (English any, Italian qualunque) have existential base meaning but universal surface force due to obligatory exhaustification. Existential FCIs (German irgendein, Farsi yek-i, Romanian vreun) retain narrow existential force. The flavor is a Chierchia-tradition typological dimension consumed by paper-specific studies (e.g., [Chi06], [AOM25a]).
- existential : FCIFlavor
Existential FCIs: irgendein, yek-i, vreun
- universal : FCIFlavor
Universal FCIs: any, qualunque, whatever
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- Chierchia2013.instDecidableEqFCIFlavor x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Chierchia2013.instReprFCIFlavor = { reprPrec := Chierchia2013.instReprFCIFlavor.repr }
Universal FCI grammaticality prediction.
Ungrammatical only in positive episodic (UE without rescue).
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- Chierchia2013.ufciGrammatical Chierchia2013.UFCIContext.positiveEpisodic = false
- Chierchia2013.ufciGrammatical Chierchia2013.UFCIContext.negation = true
- Chierchia2013.ufciGrammatical Chierchia2013.UFCIContext.conditionalAntecedent = true
- Chierchia2013.ufciGrammatical Chierchia2013.UFCIContext.deonticModal = true
- Chierchia2013.ufciGrammatical Chierchia2013.UFCIContext.epistemicModal = true
- Chierchia2013.ufciGrammatical Chierchia2013.UFCIContext.generic = true
- Chierchia2013.ufciGrammatical Chierchia2013.UFCIContext.question = true
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Reading obtained by Universal FCI in context.
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- Chierchia2013.ufciReading Chierchia2013.UFCIContext.positiveEpisodic = none
- Chierchia2013.ufciReading Chierchia2013.UFCIContext.negation = some Chierchia2013.UFCIReading.plainExistential
- Chierchia2013.ufciReading Chierchia2013.UFCIContext.conditionalAntecedent = some Chierchia2013.UFCIReading.plainExistential
- Chierchia2013.ufciReading Chierchia2013.UFCIContext.deonticModal = some Chierchia2013.UFCIReading.freeChoice
- Chierchia2013.ufciReading Chierchia2013.UFCIContext.epistemicModal = some Chierchia2013.UFCIReading.freeChoice
- Chierchia2013.ufciReading Chierchia2013.UFCIContext.generic = some Chierchia2013.UFCIReading.freeChoice
- Chierchia2013.ufciReading Chierchia2013.UFCIContext.question = some Chierchia2013.UFCIReading.plainExistential
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In DE contexts, exhaustifying "any"'s alternatives yields entailments, so the exhaustification is vacuous and "any" = plain existential.
This explains the NPI distribution of "any".
"I didn't see any students" ≡ "I didn't see a student"
The "any" contributes no special meaning in DE contexts.
Under modals, "any" yields free choice via exhaustification.
"You may read any book" = For each book x, you may read x
Modal insertion is the rescue mechanism for Universal FCIs.
"*There are any cookies" is ungrammatical.
Domain alternative exhaustification in UE episodic context yields contradiction.
The failure mechanism: exhaustification is G-contradictory. (See Core.Analyticity for G-triviality/L-analyticity)
An "any" distribution example.
- sentence : String
- context : UFCIContext
- grammatical : Bool
- reading : Option String
- notes : String
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- Chierchia2013.instReprAnyExample = { reprPrec := Chierchia2013.instReprAnyExample.repr }
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