Nandao-Q Empirical Data

@cite{zheng-2025}

Theory-neutral data on Mandarin nandao-question felicity. The core finding is that positive evidential bias is necessary for nandao-Q felicity, while negative epistemic bias is neither necessary nor sufficient.

Key Generalizations

1. Positive evidential bias (contextual evidence for p) → nandao felicitous
2. Epistemic bias alone (prior belief against p, no evidence) → nandao infelicitous
3. Evidence must be unexpected relative to prior information state
4. Nandao-Qs can function as pure inquiry (no prior belief required)

structure Phenomena.Questions.NandaoQs.NandaoDatum : Type

A nandao-Q felicity datum.

• exampleNum : String

  Example number from @cite{zheng-2025}

• context : String

  Context description

• sentence : String

  The nandao-Q sentence (pinyin)

• evidentialBias : Bool

  Is there positive evidential bias (contextual evidence for p)?

• epistemicBias : Bool

  Is there negative epistemic bias (prior belief against p)?

• unexpectedEvidence : Bool

  Is the evidence unexpected?

• felicitous : Bool

  Is the nandao-Q felicitous?

instance Phenomena.Questions.NandaoQs.instReprNandaoDatum : Repr NandaoDatum

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• Phenomena.Questions.NandaoQs.instReprNandaoDatum = { reprPrec := Phenomena.Questions.NandaoQs.instReprNandaoDatum.repr }

def Phenomena.Questions.NandaoQs.instReprNandaoDatum.repr : NandaoDatum → ℕ → Std.Format

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instance Phenomena.Questions.NandaoQs.instDecidableEqNandaoDatum : DecidableEq NandaoDatum

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• Phenomena.Questions.NandaoQs.instDecidableEqNandaoDatum = Phenomena.Questions.NandaoQs.instDecidableEqNandaoDatum.decEq

def Phenomena.Questions.NandaoQs.instDecidableEqNandaoDatum.decEq (x✝ x✝¹ : NandaoDatum) : Decidable (x✝ = x✝¹)

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def Phenomena.Questions.NandaoQs.instBEqNandaoDatum.beq : NandaoDatum → NandaoDatum → Bool

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• Phenomena.Questions.NandaoQs.instBEqNandaoDatum.beq x✝¹ x✝ = false

instance Phenomena.Questions.NandaoQs.instBEqNandaoDatum : BEq NandaoDatum

Equations

• Phenomena.Questions.NandaoQs.instBEqNandaoDatum = { beq := Phenomena.Questions.NandaoQs.instBEqNandaoDatum.beq }

def Phenomena.Questions.NandaoQs.rhetoricalUse : NandaoDatum

Ex. 1: Rhetorical use. Lee working on Sunday (evidence) contradicts B's norm that people don't work Sundays (epistemic/deontic bias).

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def Phenomena.Questions.NandaoQs.biasedUse : NandaoDatum

Ex. 2: Biased question. A believes not-raining; B enters with dripping raincoat (evidence contradicting belief).

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def Phenomena.Questions.NandaoQs.pureInquiry : NandaoDatum

Ex. 3: Pure inquiry (NOVEL). Same evidence as ex. 2 but A has NO prior belief about the weather. Nandao is still felicitous.

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def Phenomena.Questions.NandaoQs.epistemicOnly : NandaoDatum

Ex. 4a: Epistemic bias without evidence. Speaker believes room is empty but has no contextual evidence either way.

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def Phenomena.Questions.NandaoQs.evidenceNoBelief : NandaoDatum

Ex. 5 ctx 1: Evidence + no belief → felicitous.

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def Phenomena.Questions.NandaoQs.noEvidenceNoBelief : NandaoDatum

Ex. 5 ctx 2: No evidence + no belief → infelicitous.

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def Phenomena.Questions.NandaoQs.beliefNoEvidence : NandaoDatum

Ex. 5 ctx 3: No evidence + epistemic bias → infelicitous.

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def Phenomena.Questions.NandaoQs.unexpectedEvidence_ : NandaoDatum

Ex. 6 ctx 1: Unexpected evidence → felicitous.

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def Phenomena.Questions.NandaoQs.expectedEvidence : NandaoDatum

Ex. 6 ctx 2: Expected evidence → infelicitous.

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def Phenomena.Questions.NandaoQs.allData : List NandaoDatum

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theorem Phenomena.Questions.NandaoQs.evidential_bias_necessary : ((List.filter (fun (x : NandaoDatum) => x.felicitous) allData).all fun (x : NandaoDatum) => x.evidentialBias) = true

Generalization 1: All felicitous nandao-Qs have evidential bias.

theorem Phenomena.Questions.NandaoQs.epistemic_bias_not_necessary : (List.filter (fun (d : NandaoDatum) => d.felicitous && !d.epistemicBias) allData).length > 0

Generalization 2: Some felicitous nandao-Qs lack epistemic bias (the pure inquiry use).

theorem Phenomena.Questions.NandaoQs.epistemic_bias_not_sufficient : (List.filter (fun (d : NandaoDatum) => d.epistemicBias && !d.felicitous) allData).length > 0

Generalization 3: Some infelicitous nandao-Qs have epistemic bias (epistemic bias is not sufficient).

theorem Phenomena.Questions.NandaoQs.unexpectedness_necessary : ((List.filter (fun (x : NandaoDatum) => x.felicitous) allData).all fun (x : NandaoDatum) => x.unexpectedEvidence) = true

Generalization 4: All felicitous nandao-Qs have unexpected evidence.

theorem Phenomena.Questions.NandaoQs.dataset_size : allData.length = 9

9 data points from 6 examples covering 4 conditions.