Documentation

Linglib.Semantics.Questions.Bias.Defs

Polar Question Bias — vocabulary #

[Rom24] [RH04] [Lad81] [BG00]

Theory-neutral vocabulary for polar question bias, shared by lexical fragments and the theory layer. Polar questions come in three forms — PosQ, LoNQ, HiNQ — sensitive to two independent bias dimensions: original speaker bias (the speaker's prior epistemic lean) and contextual evidence bias (evidence available in the current discourse).

This file carries only the directional enums and the form/bias compatibility tables, so that Fragment lexical entries can record which bias a particle requires without importing the modal machinery (VERUM/FALSUM, □_ev) that lives in Semantics.Questions.Bias.Basic.

Main definitions #

PQForm — the three polar-question forms.
OriginalBias, ContextualEvidence — the two directional bias dimensions.
EvidentialBiasStrength — strength of contextual-evidence bias by negation scope.
originalBiasOK, evidenceBiasOK — Romero's compatibility tables.

inductive Semantics.Questions.Bias.PQForm :

The three polar question forms ([Rom24] §1).

These forms are cross-linguistically attested and constitute the fundamental typology for polar question bias research.

PosQ : PQForm
Positive question: [p?]. "Is Jane coming?"
LoNQ : PQForm
Low negation question: [not p?]. "Is Jane not coming?"
HiNQ : PQForm
High negation question: [n't p?]. "Isn't Jane coming?" In Czech: interrogative (VSO) word order.

Instances For

@[implicit_reducible]

instance Semantics.Questions.Bias.instDecidableEqPQForm :

DecidableEq PQForm

Equations

Semantics.Questions.Bias.instDecidableEqPQForm x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Semantics.Questions.Bias.instReprPQForm.repr :

PQForm → Nat → Std.Format

Equations

One or more equations did not get rendered due to their size.

Instances For

@[implicit_reducible]

instance Semantics.Questions.Bias.instReprPQForm :

Equations

Semantics.Questions.Bias.instReprPQForm = { reprPrec := Semantics.Questions.Bias.instReprPQForm.repr }

inductive Semantics.Questions.Bias.OriginalBias :

Original speaker bias: belief or expectation that p is true, based on the speaker's epistemic state prior to the current situation and exchange.

forP : OriginalBias
Speaker originally expected/believed p.
neutral : OriginalBias
Speaker had no prior expectation about p.
againstP : OriginalBias
Speaker originally expected/believed ¬p.

Instances For

@[implicit_reducible]

instance Semantics.Questions.Bias.instDecidableEqOriginalBias :

DecidableEq OriginalBias

Equations

Semantics.Questions.Bias.instDecidableEqOriginalBias x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Semantics.Questions.Bias.instReprOriginalBias.repr :

OriginalBias → Nat → Std.Format

Equations

One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Semantics.Questions.Bias.instReprOriginalBias :

Repr OriginalBias

Equations

Semantics.Questions.Bias.instReprOriginalBias = { reprPrec := Semantics.Questions.Bias.instReprOriginalBias.repr }

inductive Semantics.Questions.Bias.ContextualEvidence :

Contextual evidence bias ([BG00]): expectation about p induced by evidence available in the current discourse situation. A felicity condition on rising declaratives and a bias dimension for polar questions.

forP : ContextualEvidence
Current context provides evidence for p.
neutral : ContextualEvidence
No contextual evidence either way.
againstP : ContextualEvidence
Current context provides evidence against p.

Instances For

@[implicit_reducible]

instance Semantics.Questions.Bias.instDecidableEqContextualEvidence :

DecidableEq ContextualEvidence

Equations

Semantics.Questions.Bias.instDecidableEqContextualEvidence x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Semantics.Questions.Bias.instReprContextualEvidence.repr :

ContextualEvidence → Nat → Std.Format

Equations

One or more equations did not get rendered due to their size.

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@[implicit_reducible]

instance Semantics.Questions.Bias.instReprContextualEvidence :

Repr ContextualEvidence

Equations

Semantics.Questions.Bias.instReprContextualEvidence = { reprPrec := Semantics.Questions.Bias.instReprContextualEvidence.repr }

inductive Semantics.Questions.Bias.EvidentialBiasStrength :

Strength of contextual-evidence bias associated with a negation scope, bridging Romero's typology to Staňková's three-way Czech distinction: inner negation → strong (□_ev(¬p)), medial → weak (¬□_ev(p)), outer (FALSUM) → no □_ev involvement.

strong : EvidentialBiasStrength
Inner: □_ev(¬p).
weak : EvidentialBiasStrength
Medial: ¬□_ev(p).
none_ : EvidentialBiasStrength
Outer: FALSUM, not □_ev-based.

Instances For

@[implicit_reducible]

instance Semantics.Questions.Bias.instDecidableEqEvidentialBiasStrength :

DecidableEq EvidentialBiasStrength

Equations

Semantics.Questions.Bias.instDecidableEqEvidentialBiasStrength x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Semantics.Questions.Bias.instReprEvidentialBiasStrength :

Repr EvidentialBiasStrength

Equations

Semantics.Questions.Bias.instReprEvidentialBiasStrength = { reprPrec := Semantics.Questions.Bias.instReprEvidentialBiasStrength.repr }

def Semantics.Questions.Bias.instReprEvidentialBiasStrength.repr :

EvidentialBiasStrength → Nat → Std.Format

Equations

One or more equations did not get rendered due to their size.

Instances For

def Semantics.Questions.Bias.originalBiasOK :

PQForm → OriginalBias → Bool

Original speaker bias conditions on PQ forms ([Rom24] Table 1).

Only HiNQ mandatorily conveys original speaker bias for p. LoNQ can convey bias for p but can also be neutral. PosQ is compatible with bias for ¬p or neutrality but was not tested for bias for p.

Equations

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theorem Semantics.Questions.Bias.hiNQ_requires_bias_for_p :

originalBiasOK PQForm.HiNQ OriginalBias.neutral = false ∧ originalBiasOK PQForm.HiNQ OriginalBias.againstP = false ∧ originalBiasOK PQForm.HiNQ OriginalBias.forP = true

HiNQs mandatorily convey original speaker bias for p ([Lad81], [RH04]).

theorem Semantics.Questions.Bias.posQ_neutral_ok :

originalBiasOK PQForm.PosQ OriginalBias.neutral = true

PosQs can be used in neutral contexts.

theorem Semantics.Questions.Bias.loNQ_neutral_ok :

originalBiasOK PQForm.LoNQ OriginalBias.neutral = true

LoNQs can be neutral.

def Semantics.Questions.Bias.evidenceBiasOK :

PQForm → ContextualEvidence → Bool

Contextual evidence bias conditions on PQ forms ([Rom24] Table 2, [BG00]).

PosQ requires evidence for p (or neutral). LoNQ requires evidence against p. Outer-HiNQ is felicitous with neutral or against-p evidence.

Equations

Instances For

theorem Semantics.Questions.Bias.loNQ_requires_evidence_against_p :

evidenceBiasOK PQForm.LoNQ ContextualEvidence.forP = false ∧ evidenceBiasOK PQForm.LoNQ ContextualEvidence.neutral = false ∧ evidenceBiasOK PQForm.LoNQ ContextualEvidence.againstP = true

LoNQs require contextual evidence against p ([BG00]).

theorem Semantics.Questions.Bias.hiNQ_evidence_against_ok :

evidenceBiasOK PQForm.HiNQ ContextualEvidence.againstP = true

HiNQs are felicitous with evidence against p (contradiction scenarios).

theorem Semantics.Questions.Bias.hiNQ_evidence_neutral_ok :

evidenceBiasOK PQForm.HiNQ ContextualEvidence.neutral = true

HiNQs are also felicitous with neutral evidence (suggestion scenarios).