Homogeneity: Empirical Data

@cite{kriz-2015} @cite{kriz-spector-2021} @cite{lobner-2000}

Theory-neutral empirical patterns for homogeneity gaps in natural language.

Phenomena Covered

1. Plural definites: "The doors are open" / "The doors aren't open"
2. Conjunctions: "Ann and Bert have red hair"
3. Summative predicates: "The flag is blue"
4. Conditionals: "They play if the sun shines"
5. Collective predicates: "The teachers met"

Observation

Homogeneity is characterized by non-complementary truth conditions:

• Positive: requires universal (or near-universal) satisfaction
• Negative: requires existential denial (none satisfy)
• Gap: some but not all satisfy → neither clearly true nor false

inductive Phenomena.Plurals.Homogeneity.HomogeneityJudgment : Type

Judgment type for homogeneity scenarios.

• clearlyTrue : HomogeneityJudgment
• clearlyFalse : HomogeneityJudgment
• neitherTrueNorFalse : HomogeneityJudgment
• marginal : HomogeneityJudgment

instance Phenomena.Plurals.Homogeneity.instReprHomogeneityJudgment : Repr HomogeneityJudgment

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• Phenomena.Plurals.Homogeneity.instReprHomogeneityJudgment = { reprPrec := Phenomena.Plurals.Homogeneity.instReprHomogeneityJudgment.repr }

def Phenomena.Plurals.Homogeneity.instReprHomogeneityJudgment.repr : HomogeneityJudgment → Nat → Std.Format

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instance Phenomena.Plurals.Homogeneity.instDecidableEqHomogeneityJudgment : DecidableEq HomogeneityJudgment

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• Phenomena.Plurals.Homogeneity.instDecidableEqHomogeneityJudgment x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

structure Phenomena.Plurals.Homogeneity.HomogeneityDatum : Type

Basic homogeneity datum: a sentence pair showing the gap.

• positiveSentence : String

  The positive sentence

• negativeSentence : String

  The negative sentence

• allScenario : String

  Description of the "all" scenario

• noneScenario : String

  Description of the "none" scenario

• gapScenario : String

  Description of the "some but not all" scenario

• positiveInAll : HomogeneityJudgment

  Judgment in all scenario

• negativeInAll : HomogeneityJudgment
• positiveInNone : HomogeneityJudgment

  Judgment in none scenario

• negativeInNone : HomogeneityJudgment
• positiveInGap : HomogeneityJudgment

  Judgment in gap scenario

• negativeInGap : HomogeneityJudgment

def Phenomena.Plurals.Homogeneity.instReprHomogeneityDatum.repr : HomogeneityDatum → Nat → Std.Format

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instance Phenomena.Plurals.Homogeneity.instReprHomogeneityDatum : Repr HomogeneityDatum

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• Phenomena.Plurals.Homogeneity.instReprHomogeneityDatum = { reprPrec := Phenomena.Plurals.Homogeneity.instReprHomogeneityDatum.repr }

def Phenomena.Plurals.Homogeneity.switchesExample : HomogeneityDatum

The canonical example: "The switches are on."

In a scenario with 10 switches:

• All on: positive true, negative false
• None on: positive false, negative true
• 5 on: neither clearly true nor false

Source: @cite{kriz-2015}, @cite{kriz-chemla-2015}

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def Phenomena.Plurals.Homogeneity.booksExample : HomogeneityDatum

Books example from @cite{kriz-chemla-2015} experimental design.

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def Phenomena.Plurals.Homogeneity.conjunctionExample : HomogeneityDatum

Conjunctions exhibit homogeneity but resist non-maximal readings.

"Ann and Bert have red hair" behaves like a plural definite for homogeneity, but unlike plural definites, it resists non-maximal readings.

Source: @cite{schwarzschild-1996}, @cite{kriz-2015}

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structure Phenomena.Plurals.Homogeneity.ConjunctionVsPluralDatum : Type

The contrast between conjunctions and plural definites for non-maximality.

Source: @cite{brisson-1998}, @cite{kriz-2015}

• conjunctionSentence : String

  The conjunction sentence

• pluralSentence : String

  The plural definite sentence

• context : String

  Context description

• conjunctionPermitsNonMax : Bool

  Does the conjunction permit non-maximal reading?

• pluralPermitsNonMax : Bool

  Does the plural permit non-maximal reading?

def Phenomena.Plurals.Homogeneity.instReprConjunctionVsPluralDatum.repr : ConjunctionVsPluralDatum → Nat → Std.Format

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instance Phenomena.Plurals.Homogeneity.instReprConjunctionVsPluralDatum : Repr ConjunctionVsPluralDatum

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• Phenomena.Plurals.Homogeneity.instReprConjunctionVsPluralDatum = { reprPrec := Phenomena.Plurals.Homogeneity.instReprConjunctionVsPluralDatum.repr }

def Phenomena.Plurals.Homogeneity.coworkersExample : ConjunctionVsPluralDatum

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def Phenomena.Plurals.Homogeneity.summativeExample : HomogeneityDatum

Summative predicates: apply to parts of a singular entity.

"The flag is blue" requires all (salient) parts to be blue.

Source: @cite{lobner-2000}, @cite{kriz-2015},

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def Phenomena.Plurals.Homogeneity.conditionalExample : HomogeneityDatum

Bare conditionals exhibit homogeneity over situations.

Source: @cite{von-fintel-1997}, @cite{gajewski-2005}, @cite{kriz-2015}

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def Phenomena.Plurals.Homogeneity.collectiveExample : HomogeneityDatum

Collective predicates: "The teachers met."

Homogeneity concerns whether all teachers participated in a meeting, or just some subgroup.

Source: @cite{kriz-2015}, @cite{kriz-2016}

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structure Phenomena.Plurals.Homogeneity.UpwardHomogeneityDatum : Type

"Upward homogeneity" in collective predication.

When a plurality is part of a larger group that satisfies a collective predicate, the smaller plurality is neither clearly a satisfier nor clearly not.

Source: @cite{kriz-2015}, @cite{kriz-2016},

• sentence : String

  The sentence

• scenario : String

  Scenario description

• judgment : HomogeneityJudgment

  Judgment

instance Phenomena.Plurals.Homogeneity.instReprUpwardHomogeneityDatum : Repr UpwardHomogeneityDatum

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• Phenomena.Plurals.Homogeneity.instReprUpwardHomogeneityDatum = { reprPrec := Phenomena.Plurals.Homogeneity.instReprUpwardHomogeneityDatum.repr }

def Phenomena.Plurals.Homogeneity.instReprUpwardHomogeneityDatum.repr : UpwardHomogeneityDatum → Nat → Std.Format

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def Phenomena.Plurals.Homogeneity.hamletExample : UpwardHomogeneityDatum

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def Phenomena.Plurals.Homogeneity.soldiersExample : UpwardHomogeneityDatum

@cite{kriz-spector-2021} §3.3, example (31): "The soldiers of my brigade didn't surround the castle." False when half the brigade surrounded the castle WITH other soldiers — the predicate's truth leaks upward through mereological overlap.

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inductive Phenomena.Plurals.Homogeneity.HomogeneityRemover : Type

Elements that remove homogeneity gaps.

• all : HomogeneityRemover
• both : HomogeneityRemover
• every : HomogeneityRemover
• each : HomogeneityRemover
• completely : HomogeneityRemover
• necessarily : HomogeneityRemover

def Phenomena.Plurals.Homogeneity.instReprHomogeneityRemover.repr : HomogeneityRemover → Nat → Std.Format

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instance Phenomena.Plurals.Homogeneity.instReprHomogeneityRemover : Repr HomogeneityRemover

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• Phenomena.Plurals.Homogeneity.instReprHomogeneityRemover = { reprPrec := Phenomena.Plurals.Homogeneity.instReprHomogeneityRemover.repr }

instance Phenomena.Plurals.Homogeneity.instDecidableEqHomogeneityRemover : DecidableEq HomogeneityRemover

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• Phenomena.Plurals.Homogeneity.instDecidableEqHomogeneityRemover x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

structure Phenomena.Plurals.Homogeneity.HomogeneityRemovalDatum : Type

Datum showing homogeneity removal.

• homogeneousSentence : String

  Sentence with homogeneity

• precisesentence : String

  Sentence with homogeneity removed

• remover : HomogeneityRemover

  What removes homogeneity

• gapScenario : String

  Gap scenario

• homogeneousJudgment : HomogeneityJudgment

  Judgment for homogeneous sentence in gap

• preciseJudgment : HomogeneityJudgment

  Judgment for precise sentence in gap

def Phenomena.Plurals.Homogeneity.instReprHomogeneityRemovalDatum.repr : HomogeneityRemovalDatum → Nat → Std.Format

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instance Phenomena.Plurals.Homogeneity.instReprHomogeneityRemovalDatum : Repr HomogeneityRemovalDatum

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• Phenomena.Plurals.Homogeneity.instReprHomogeneityRemovalDatum = { reprPrec := Phenomena.Plurals.Homogeneity.instReprHomogeneityRemovalDatum.repr }

def Phenomena.Plurals.Homogeneity.allRemovesHomogeneity : HomogeneityRemovalDatum

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def Phenomena.Plurals.Homogeneity.bothRemovesHomogeneity : HomogeneityRemovalDatum

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def Phenomena.Plurals.Homogeneity.completelyRemovesHomogeneity : HomogeneityRemovalDatum

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structure Phenomena.Plurals.Homogeneity.QuestionAnswerDatum : Type

Responses to questions in gap scenarios.

Neither "yes" nor "no" is fully appropriate.

Source: @cite{kriz-2015}

• question : String

  The question

• scenario : String

  Gap scenario

• yesAppropriate : Bool

  Is "Yes" appropriate?

• noAppropriate : Bool

  Is "No" appropriate?

• betterResponse : String

  Better response

instance Phenomena.Plurals.Homogeneity.instReprQuestionAnswerDatum : Repr QuestionAnswerDatum

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• Phenomena.Plurals.Homogeneity.instReprQuestionAnswerDatum = { reprPrec := Phenomena.Plurals.Homogeneity.instReprQuestionAnswerDatum.repr }

def Phenomena.Plurals.Homogeneity.instReprQuestionAnswerDatum.repr : QuestionAnswerDatum → Nat → Std.Format

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def Phenomena.Plurals.Homogeneity.booksQuestionExample : QuestionAnswerDatum

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structure Phenomena.Plurals.Homogeneity.HomogeneityGeneralizations : Type

Core empirical generalizations about homogeneity.

• positiveUniversal : Bool

  Positive sentences get universal-like truth conditions

• negativeExistential : Bool

  Negative sentences get existential-like falsity conditions

• gapYieldsNeither : Bool

  Gap scenarios yield neither-true-nor-false judgments

• quantifiersRemoveGap : Bool

  All/both/every remove the gap

• conjunctionsResistNonMax : Bool

  Conjunctions have gaps but resist non-maximality

instance Phenomena.Plurals.Homogeneity.instReprHomogeneityGeneralizations : Repr HomogeneityGeneralizations

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• Phenomena.Plurals.Homogeneity.instReprHomogeneityGeneralizations = { reprPrec := Phenomena.Plurals.Homogeneity.instReprHomogeneityGeneralizations.repr }

def Phenomena.Plurals.Homogeneity.instReprHomogeneityGeneralizations.repr : HomogeneityGeneralizations → Nat → Std.Format

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def Phenomena.Plurals.Homogeneity.mainGeneralizations : HomogeneityGeneralizations

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def Phenomena.Plurals.Homogeneity.pluralDefiniteExamples : List HomogeneityDatum

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• Phenomena.Plurals.Homogeneity.pluralDefiniteExamples = [Phenomena.Plurals.Homogeneity.switchesExample, Phenomena.Plurals.Homogeneity.booksExample]

def Phenomena.Plurals.Homogeneity.otherHomogeneityExamples : List HomogeneityDatum

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def Phenomena.Plurals.Homogeneity.removalExamples : List HomogeneityRemovalDatum

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