Documentation

Studies.RonderosEtAl2024

Ronderos et al. (2024): Factors affecting contrastive inferences #

A listener who interprets the short pencil contrastively, as distinguishing the pencil from a longer one, identifies the referent before the noun when the display holds such a contrasting object. Ronderos and colleagues track this contrastive inference by eye-tracking with colour, scalar and material adjectives, in Sedivy's paradigm, and separate three accounts by their predictions across adjective types. On Sedivy's pragmatic account the interpretation is contrastive only for adjectives rarely used descriptively, so colour should show no contrast effect and material should. On the perceptual account the contrast must be perceived during preview, and material contrasts are less salient, so colour should show the effect and material should not. On the semantic account of Aparicio, Xiang and Kennedy a relative gradable adjective needs a comparison class from the display, which lowers the no-contrast baseline for scalar adjectives.

Main statements #

perceptual_matches: the perceptual account predicts the effects found.
pragmatic_fails: the pragmatic account does not.
baseline_higher_iff_not_relative: the baseline is higher exactly for the non-gradable adjective types.

Implementation notes #

Kinds of object are named by a representative object. The perceptual factor attributes a property to a whole kind as soon as one member shows it, so that objects of a kind are never perceived as contrasting.
Salience and informativity are the paper's premises per adjective type, with size contrasts taken as perceptible, as the replicated scalar effect requires.
The findings are the statistics of the Results section, in Data/Experiments/RonderosEtAl2024.json, pooled over English, Hindi and Hungarian, which the paper's models treat as a grouping unit only. An effect is significant when its printed p-value is below 0.05.

References #

The paradigm (Figure 1) #

inductive RonderosEtAl2024.Object :

The four objects of a display are the target, the object that in the contrast condition is of the target's kind and lacks the property, the competitor of another kind sharing it, and a distractor.

target : Object
contrastingObject : Object
competitor : Object
distractor : Object

Instances For

@[instance_reducible]

instance RonderosEtAl2024.instDecidableEqObject :

DecidableEq Object

Equations

RonderosEtAl2024.instDecidableEqObject x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def RonderosEtAl2024.instReprObject.repr :

Object → ℕ → Std.Format

Equations

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

Instances For

@[instance_reducible]

instance RonderosEtAl2024.instReprObject :

Equations

RonderosEtAl2024.instReprObject = { reprPrec := RonderosEtAl2024.instReprObject.repr }

@[instance_reducible]

instance RonderosEtAl2024.instFintypeObject :

Fintype Object

Equations

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

structure RonderosEtAl2024.Display :

A display, as the listener takes it in, records the kind of each object, named by a representative, and the objects showing the adjective's property.

kind : Object → Object
has : Finset Object

Instances For

def RonderosEtAl2024.Display.descriptive (d : Display) :

Finset Object

The descriptive interpretation of the adjective picks out the objects with the property.

Equations

d.descriptive = d.has

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def RonderosEtAl2024.Display.contrastive (d : Display) :

Finset Object

The contrastive interpretation picks out the objects with the property that an object of their kind lacks.

Equations

d.contrastive = {o ∈ d.has | ∃ (o' : RonderosEtAl2024.Object), d.kind o' = d.kind o ∧ o' ∉ d.has}

Instances For

theorem RonderosEtAl2024.Display.contrastive_subset_descriptive (d : Display) :

d.contrastive ⊆ d.descriptive

def RonderosEtAl2024.Display.blur (d : Display) :

A property whose contrast is not perceived is taken in by attributing it to a whole kind as soon as one of its members shows it.

Equations

d.blur = { kind := d.kind, has := {o : RonderosEtAl2024.Object | ∃ (o' : RonderosEtAl2024.Object), d.kind o' = d.kind o ∧ o' ∈ d.has} }

Instances For

theorem RonderosEtAl2024.Display.contrastive_blur (d : Display) :

d.blur.contrastive = ∅

A blurred display never shows a contrast within a kind.

def RonderosEtAl2024.Anticipates (S : Finset Object) :

An interpretation anticipates the noun when the definite description already refers under it, and to the target.

Equations

RonderosEtAl2024.Anticipates S = ((Reference.iota fun (x : RonderosEtAl2024.Object) => x ∈ S) = some RonderosEtAl2024.Object.target)

Instances For

theorem RonderosEtAl2024.anticipates_iff {S : Finset Object} :

Anticipates S ↔ S = {Object.target}

An interpretation anticipates the noun exactly when it is the target alone.

@[instance_reducible]

instance RonderosEtAl2024.instDecidableAnticipates (S : Finset Object) :

Decidable (Anticipates S)

Equations

RonderosEtAl2024.instDecidableAnticipates S = decidable_of_iff (S = {RonderosEtAl2024.Object.target}) ⋯

def RonderosEtAl2024.contrastDisplay :

In the display of the contrast condition the contrasting object is of the target's kind and lacks the property, and the competitor has it.

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

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def RonderosEtAl2024.noContrastDisplay :

In the display of the no-contrast condition the contrasting object is replaced by a distractor of its own kind.

Equations

RonderosEtAl2024.noContrastDisplay = { kind := fun (o : RonderosEtAl2024.Object) => o, has := {RonderosEtAl2024.Object.target, RonderosEtAl2024.Object.competitor} }

Instances For

def RonderosEtAl2024.display :

Condition → Display

The display of each condition.

Equations

Instances For

theorem RonderosEtAl2024.contrastive_contrast :

contrastDisplay.contrastive = {Object.target}

The contrastive interpretation of the contrast display singles out the target before the noun, since the competitor has the property but no object of its kind lacks it.

theorem RonderosEtAl2024.descriptive_contrast :

contrastDisplay.descriptive = {Object.target, Object.competitor}

The descriptive interpretation leaves the target and the competitor.

theorem RonderosEtAl2024.contrastive_noContrast :

noContrastDisplay.contrastive = ∅

Without a contrasting object the contrastive interpretation finds nothing.

theorem RonderosEtAl2024.descriptive_noContrast :

noContrastDisplay.descriptive = {Object.target, Object.competitor}

The three factors #

def RonderosEtAl2024.Salient :

AdjType → Prop

An adjective type is salient when a contrast in its property is visually salient during preview. Material contrasts are not ([KD21], [JERF22]), and colour and size contrasts are.

Equations

Instances For

@[instance_reducible]

instance RonderosEtAl2024.instDecidablePredAdjTypeSalient :

DecidablePred Salient

Equations

def RonderosEtAl2024.Informative :

AdjType → Prop

An adjective type is informative when it is rarely used descriptively, so that its use is expected to be informative. Colour adjectives are produced descriptively about half the time ([Sed04]), material and scalar ones rarely.

Equations

Instances For

@[instance_reducible]

instance RonderosEtAl2024.instDecidablePredAdjTypeInformative :

DecidablePred Informative

Equations

def RonderosEtAl2024.AdjType.adjectiveClass :

AdjType → Degree.AdjectiveClass

Scalar adjectives are relative gradable, and colour and material adjectives are non-gradable ([Ken07b]).

Equations

Instances For

The accounts of the contrast effect #

structure RonderosEtAl2024.Account :

An account fixes, per adjective type, how the display is perceived and how the adjective is interpreted.

perceive : AdjType → Display → Display
interpret : AdjType → Display → Finset Object

Instances For

def RonderosEtAl2024.pragmatic :

On the pragmatic account ([Sed03], [Sed04]) perception is veridical, and the adjective is interpreted contrastively only when it is expected to be informative.

Equations

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Instances For

def RonderosEtAl2024.perceptual :

On the perceptual account the adjective is always interpreted contrastively, but a contrast that is not salient is not perceived.

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Instances For

def RonderosEtAl2024.Account.PredictsEffect (a : Account) (t : AdjType) :

An account predicts a contrast effect for an adjective type when the noun is anticipated in the contrast condition and not in the no-contrast one.

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@[instance_reducible]

instance RonderosEtAl2024.instDecidablePredictsEffect (a : Account) (t : AdjType) :

Decidable (a.PredictsEffect t)

Equations

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theorem RonderosEtAl2024.pragmatic_predictsEffect_iff (t : AdjType) :

pragmatic.PredictsEffect t ↔ Informative t

The pragmatic account predicts a contrast effect exactly for the informative types.

theorem RonderosEtAl2024.perceptual_predictsEffect_iff (t : AdjType) :

perceptual.PredictsEffect t ↔ Salient t

The perceptual account predicts a contrast effect exactly for the salient contrasts.

The findings #

def RonderosEtAl2024.Bound.Significant :

Bound → Data.Experiments.Decimal → Prop

A printed p-value is below 0.05 when it is an upper bound at most 0.05 or a value under it.

Equations

RonderosEtAl2024.Bound.below.Significant x✝ = (x✝.toRat ≤ 5 / 100)
RonderosEtAl2024.Bound.exact.Significant x✝ = (x✝.toRat < 5 / 100)

Instances For

@[instance_reducible]

instance RonderosEtAl2024.instDecidableSignificant (b : Bound) (p : Data.Experiments.Decimal) :

Decidable (b.Significant p)

Equations

def RonderosEtAl2024.Effect (t : AdjType) :

The paper found a contrast effect for an adjective type when it reports a significant cluster of condition effects on target looks in the noun window and a significant effect of condition on the target-advantage score.

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@[instance_reducible]

instance RonderosEtAl2024.instDecidablePredAdjTypeEffect :

DecidablePred Effect

Equations

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

def RonderosEtAl2024.BaselineHigherThanScalar (t : AdjType) :

Whether looks to the target and the competitor in the no-contrast baseline were significantly higher for an adjective type than for scalar adjectives, the intercept of the model.

Equations

RonderosEtAl2024.BaselineHigherThanScalar t = ∃ r ∈ RonderosEtAl2024.baselineLooks, r.adjType = t ∧ 0 < r.beta.toRat ∧ r.bound.Significant r.p

Instances For

@[instance_reducible]

instance RonderosEtAl2024.instDecidablePredAdjTypeBaselineHigherThanScalar :

DecidablePred BaselineHigherThanScalar

Equations

RonderosEtAl2024.instDecidablePredAdjTypeBaselineHigherThanScalar x✝ = RonderosEtAl2024.instDecidablePredAdjTypeBaselineHigherThanScalar._aux_1 x✝

theorem RonderosEtAl2024.perceptual_matches (t : AdjType) :

perceptual.PredictsEffect t ↔ Effect t

The perceptual account predicts the effects found, for colour and scalar adjectives and not for material ones.

theorem RonderosEtAl2024.pragmatic_fails :

¬∀ (t : AdjType), pragmatic.PredictsEffect t ↔ Effect t

The pragmatic account predicts an effect for material and none for colour, the reverse of what was found.

theorem RonderosEtAl2024.baseline_higher_iff_not_relative (t : AdjType) :

BaselineHigherThanScalar t ↔ t.adjectiveClass ≠ Degree.AdjectiveClass.relative

The baseline follows the adjective classes. Looks to the property-matching objects exceed those for scalar adjectives exactly for the non-gradable types, which need no comparison class ([AXK15]).

theorem RonderosEtAl2024.salience_not_baseline :

¬∀ (t : AdjType), BaselineHigherThanScalar t → Salient t

Salience does not explain the baseline, since material adjectives, whose contrast is not salient, still draw more looks than scalar ones.