structure Phenomena.Questions.PolarAnswers.YesNoDatum : Type

@cite{groenendijk-stokhof-1984}: Yes and No are T⁰ (sentence adverbs, category S/S). @cite{fox-katzir-2011}

• yes ~ λp.p(a) (affirms the proposition)
• no ~ λp.¬p(a) (negates the proposition)

This makes sentential interrogatives derivable by the same IA-rule as constituent interrogatives, with AB⁰ = S and T⁰ = S/S.

• question : String

  The polar question

• answer : String

  The answer (yes/no form)

• positive : Bool

  Is this positive or negative?

• meaning : String

  The proposition expressed by the answer

• source : String

  Source

def Phenomena.Questions.PolarAnswers.instReprYesNoDatum.repr : YesNoDatum → Nat → Std.Format

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instance Phenomena.Questions.PolarAnswers.instReprYesNoDatum : Repr YesNoDatum

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• Phenomena.Questions.PolarAnswers.instReprYesNoDatum = { reprPrec := Phenomena.Questions.PolarAnswers.instReprYesNoDatum.repr }

def Phenomena.Questions.PolarAnswers.doesJohnWalk_yes : YesNoDatum

G&S p. 321: "Does John walk?"

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• Phenomena.Questions.PolarAnswers.doesJohnWalk_yes = { question := "Does John walk?", answer := "Yes", positive := true, meaning := "John walks", source := "G&S 1984, p. 321" }

def Phenomena.Questions.PolarAnswers.doesJohnWalk_no : YesNoDatum

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• Phenomena.Questions.PolarAnswers.doesJohnWalk_no = { question := "Does John walk?", answer := "No", positive := false, meaning := "John doesn't walk", source := "G&S 1984, p. 322" }

def Phenomena.Questions.PolarAnswers.yesNoExamples : List YesNoDatum

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• Phenomena.Questions.PolarAnswers.yesNoExamples = [Phenomena.Questions.PolarAnswers.doesJohnWalk_yes, Phenomena.Questions.PolarAnswers.doesJohnWalk_no]

structure Phenomena.Questions.PolarAnswers.ConditionalAnswerDatum : Type

@cite{groenendijk-stokhof-1984}, p. 324-326: A conditional answer to a polar question receives a BICONDITIONAL interpretation via exhaustification.

"Does John walk?" → "If Mary walks" means: John walks IFF Mary walks (not just: John walks IF Mary walks)

• question : String

  The polar question

• conditionalAnswer : String

  The conditional answer

• surfaceMeaning : String

  Surface form (what was said)

• exhaustifiedMeaning : String

  Exhaustified meaning (what was understood)

• source : String

  Source

instance Phenomena.Questions.PolarAnswers.instReprConditionalAnswerDatum : Repr ConditionalAnswerDatum

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• Phenomena.Questions.PolarAnswers.instReprConditionalAnswerDatum = { reprPrec := Phenomena.Questions.PolarAnswers.instReprConditionalAnswerDatum.repr }

def Phenomena.Questions.PolarAnswers.instReprConditionalAnswerDatum.repr : ConditionalAnswerDatum → Nat → Std.Format

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def Phenomena.Questions.PolarAnswers.ifMaryWalks : ConditionalAnswerDatum

G&S p. 324: Conditional becomes biconditional in answer context

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def Phenomena.Questions.PolarAnswers.conditionalAsQuestion : ConditionalAnswerDatum

When the question itself is about a conditional, no strengthening occurs

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def Phenomena.Questions.PolarAnswers.conditionalAnswerExamples : List ConditionalAnswerDatum

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• Phenomena.Questions.PolarAnswers.conditionalAnswerExamples = [Phenomena.Questions.PolarAnswers.ifMaryWalks, Phenomena.Questions.PolarAnswers.conditionalAsQuestion]

def Phenomena.Questions.PolarAnswers.conditionalBiconditionalPrinciple : String

Conditional vs biconditional reading depends on whether the question targets the conditional itself or its consequent.

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structure Phenomena.Questions.PolarAnswers.DisjunctionAnswerDatum : Type

@cite{groenendijk-stokhof-1984}, p. 327: Similar to conditionals, disjunctions in answers receive exclusive interpretation via exhaustification.

• question : String

  The polar question

• disjunctiveAnswer : String

  The disjunctive answer

• exclusive : Bool

  Inclusive or exclusive reading?

• explanation : String

  Explanation

• source : String

  Source

instance Phenomena.Questions.PolarAnswers.instReprDisjunctionAnswerDatum : Repr DisjunctionAnswerDatum

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• Phenomena.Questions.PolarAnswers.instReprDisjunctionAnswerDatum = { reprPrec := Phenomena.Questions.PolarAnswers.instReprDisjunctionAnswerDatum.repr }

def Phenomena.Questions.PolarAnswers.instReprDisjunctionAnswerDatum.repr : DisjunctionAnswerDatum → Nat → Std.Format

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def Phenomena.Questions.PolarAnswers.cookiesOrChocolates_exclusive : DisjunctionAnswerDatum

Disjunction becomes exclusive when answering about disjunct

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def Phenomena.Questions.PolarAnswers.cookiesOrChocolates_inclusive : DisjunctionAnswerDatum

Disjunction stays inclusive when answering about disjunction itself

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def Phenomena.Questions.PolarAnswers.disjunctionAnswerExamples : List DisjunctionAnswerDatum

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• Phenomena.Questions.PolarAnswers.disjunctionAnswerExamples = [Phenomena.Questions.PolarAnswers.cookiesOrChocolates_exclusive, Phenomena.Questions.PolarAnswers.cookiesOrChocolates_inclusive]

structure Phenomena.Questions.PolarAnswers.NegativeInterrogativeDatum : Type

@cite{groenendijk-stokhof-1984}, p. 331-334: Negation in interrogatives does NOT contribute to semantic content. Instead, it marks a doxastic attitude: the questioner expects a negative answer.

"Doesn't John walk?" asks the SAME question as "Does John walk?" but marks that the questioner expects "No" as the answer.

Note: sameQuestion encodes the G&S 1984 analysis. @cite{holmberg-2016} argues that positive and negative polar questions are NOT the same question: the negative question's primary proposition (the one the speaker expects) is ¬p, producing different discourse effects and cross-linguistic answer patterns. The value here reflects only the G&S view.

• positiveForm : String

  The positive form of the question

• negativeForm : String

  The negative form of the question

• sameQuestion : Bool

  Do they express the same question semantically? Note: this is the @cite{groenendijk-stokhof-1984} analysis; @cite{holmberg-2016} argues they differ.

• noMeaning : String

  What does "No" mean as an answer to the negative form?

• doxasticAttitude : String

  What attitude does the negative form mark?

• source : String

  Source

def Phenomena.Questions.PolarAnswers.instReprNegativeInterrogativeDatum.repr : NegativeInterrogativeDatum → Nat → Std.Format

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instance Phenomena.Questions.PolarAnswers.instReprNegativeInterrogativeDatum : Repr NegativeInterrogativeDatum

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• Phenomena.Questions.PolarAnswers.instReprNegativeInterrogativeDatum = { reprPrec := Phenomena.Questions.PolarAnswers.instReprNegativeInterrogativeDatum.repr }

def Phenomena.Questions.PolarAnswers.doesntJohnWalk : NegativeInterrogativeDatum

G&S p. 331: "Doesn't John walk?" vs "Does John walk?"

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def Phenomena.Questions.PolarAnswers.negativeInterrogativeExamples : List NegativeInterrogativeDatum

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• Phenomena.Questions.PolarAnswers.negativeInterrogativeExamples = [Phenomena.Questions.PolarAnswers.doesntJohnWalk]

structure Phenomena.Questions.PolarAnswers.MarkedAnswerDatum : Type

When answering against the questioner's expected polarity, the answer must be MARKED (emphatic stress, do-support).

• question : String

  The question

• expectedPolarity : Bool

  Expected answer polarity based on question form

• unmarkedAnswer : String

  Unmarked answer (goes with expectation)

• markedAnswer : String

  Marked answer (goes against expectation)

• source : String

  Source

def Phenomena.Questions.PolarAnswers.instReprMarkedAnswerDatum.repr : MarkedAnswerDatum → Nat → Std.Format

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instance Phenomena.Questions.PolarAnswers.instReprMarkedAnswerDatum : Repr MarkedAnswerDatum

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• Phenomena.Questions.PolarAnswers.instReprMarkedAnswerDatum = { reprPrec := Phenomena.Questions.PolarAnswers.instReprMarkedAnswerDatum.repr }

def Phenomena.Questions.PolarAnswers.negativeQuestion_positiveAnswer : MarkedAnswerDatum

Negative interrogative expects negative; positive answer needs marking

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def Phenomena.Questions.PolarAnswers.tagQuestion_negativeAnswer : MarkedAnswerDatum

Positive interrogative with positive marking expects positive

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def Phenomena.Questions.PolarAnswers.markedAnswerExamples : List MarkedAnswerDatum

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• Phenomena.Questions.PolarAnswers.markedAnswerExamples = [Phenomena.Questions.PolarAnswers.negativeQuestion_positiveAnswer, Phenomena.Questions.PolarAnswers.tagQuestion_negativeAnswer]

structure Phenomena.Questions.PolarAnswers.NegationVsAntonymDatum : Type

G&S p. 333: Clear evidence that negation in interrogatives is not semantic: "Are you not happy?" vs "Are you unhappy?" have different answer patterns.

• negatedForm : String

  Interrogative with negation

• antonymForm : String

  Interrogative with antonym

• noMeaning_negated : String

  What "No" means for negated form

• noMeaning_antonym : String

  What "No" means for antonym form

• sameQuestion : Bool

  Are these the same question?

• source : String

  Source

instance Phenomena.Questions.PolarAnswers.instReprNegationVsAntonymDatum : Repr NegationVsAntonymDatum

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• Phenomena.Questions.PolarAnswers.instReprNegationVsAntonymDatum = { reprPrec := Phenomena.Questions.PolarAnswers.instReprNegationVsAntonymDatum.repr }

def Phenomena.Questions.PolarAnswers.instReprNegationVsAntonymDatum.repr : NegationVsAntonymDatum → Nat → Std.Format

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def Phenomena.Questions.PolarAnswers.notHappy_vs_unhappy : NegationVsAntonymDatum

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def Phenomena.Questions.PolarAnswers.negationVsAntonymExamples : List NegationVsAntonymDatum

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• Phenomena.Questions.PolarAnswers.negationVsAntonymExamples = [Phenomena.Questions.PolarAnswers.notHappy_vs_unhappy]

def Phenomena.Questions.PolarAnswers.whyNegationIsDoxastic : String

G&S's explanation for why negation can be used non-semantically: In the semantics of interrogatives, "Does John walk?" and "Does John not walk?" express the SAME question (same partition). This opens up negation for non-semantic (doxastic) use.

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Turk, Hirsch & İnce (2026) observe that deontic modal answers are infelicitous responses to Turkish polar questions formed with mI.

"Ali uyuyor mu?" ("Does Ali sleep?")
→ "Evet" / "Hayır" — felicitous (polar answer)
→ "Ali uyumalı" ("Ali must sleep") — infelicitous (modal answer)

This is unexpected under Rooth-style type-theoretic alternative
computation, where □p has the same type as p and should be an
alternative. @cite{fox-katzir-2011} category match explains why:
*mI* is a particle (PART), modals are auxiliaries (AUX), so
category match excludes □p from the alternative set. 

def Phenomena.Questions.PolarAnswers.turkishPolar_yes : QAPair

"Ali uyuyor mu?" → "Evet" (yes) — felicitous.

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def Phenomena.Questions.PolarAnswers.turkishPolar_no : QAPair

"Ali uyuyor mu?" → "Hayır" (no) — felicitous.

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def Phenomena.Questions.PolarAnswers.turkishPolar_must : QAPair

"Ali uyuyor mu?" → "Ali uyumalı" (Ali must sleep) — infelicitous. A deontic modal answer does not address the polar question.

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def Phenomena.Questions.PolarAnswers.turkishPolarExamples : List QAPair

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theorem Phenomena.Questions.PolarAnswers.turkishPolar_modal_infelicitous : turkishPolar_must.felicitous = false

Modal answers are infelicitous to Turkish polar questions.