Documentation

Linglib.Phenomena.Presupposition.Studies.TonhauserBeaverDegen2018

@cite{tonhauser-beaver-degen-2018}: How Projective Is Projective Content? #

@cite{tonhauser-beaver-degen-2018} @cite{potts-2005} @cite{tonhauser-beaver-roberts-simons-2013}Empirical data from "How projective is projective content? Gradience in projectivity and at-issueness." Journal of Semantics 35(3): 495–542.

Key Findings #

Projectivity is gradient, not binary. Even "strong" projective triggers like NRRCs show mean projectivity ≈ .96, not 1.0.
Not-at-issueness is gradient and positively correlated with projectivity: r = .85 across 9 expression types (Exp 1a), r = .99 across 12 predicates (Exp 1b).
Appositives are not maximally projective, contra @cite{potts-2005}.
Within-type variation: different lexical items of the same type yield different ratings.

Gradient Projection Principle (GPP) #

The paper's central theoretical contribution (p. 497, ex. 7):

"If content C is expressed by a constituent embedded under an entailment-canceling operator, then C projects to the extent that it is not at-issue."

This generalizes Simons et al.'s (2010) Pragmatic Account by replacing the binary at-issue/not-at-issue distinction with a gradient one.

Experiments #

Exp 1a: 9 expression types — projectivity + not-at-issueness (asking whether diagnostic). 190 participants.
Exp 1b: 12 clause-embedding predicates — same diagnostics. 235 participants (after exclusions).
Exp 2a/2b: Replications with direct dissent diagnostic (not formalized here).

Data #

Values are approximate means read from Figures 3 and 6. The paper reports ranges in text (e.g., projectivity .76–.96 for Exp 1a) but does not provide a table of exact per-expression means. Textually confirmed values are annotated.

The scale is 0–1 (proportion of "yes" responses). The paper measures not-at-issueness via the "asking whether" diagnostic: higher values mean the content is MORE not-at-issue (more backgrounded).

inductive TonhauserBeaverDegen2018.ExpressionType :

The 9 expression types tested in Experiment 1a.

All are non-SCF (Strong Contextual Felicity = no), chosen to isolate projectivity and at-issueness variation (p. 504).

Class B (SCF=no, OLE=no): NRRC, nominal appositive, possessive NP
Class C (SCF=no, OLE=yes): discover, know, be annoyed, stop
Focus-sensitive: only
Evaluative adjective: be stupid to

nrrc : ExpressionType
nominalAppositive : ExpressionType
possessiveNP : ExpressionType
discover : ExpressionType
know : ExpressionType
annoyed : ExpressionType
stop : ExpressionType
only : ExpressionType
stupid : ExpressionType

Instances For

@[implicit_reducible]

instance TonhauserBeaverDegen2018.instDecidableEqExpressionType :

DecidableEq ExpressionType

Equations

TonhauserBeaverDegen2018.instDecidableEqExpressionType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def TonhauserBeaverDegen2018.instReprExpressionType.repr :

ExpressionType → ℕ → Std.Format

Equations

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

Instances For

@[implicit_reducible]

instance TonhauserBeaverDegen2018.instReprExpressionType :

Repr ExpressionType

Equations

TonhauserBeaverDegen2018.instReprExpressionType = { reprPrec := TonhauserBeaverDegen2018.instReprExpressionType.repr }

def TonhauserBeaverDegen2018.projectivityRating :

ExpressionType → ℚ

Mean projectivity rating from Experiment 1a (0–1 scale).

Values approximate means from Figure 3. Text (p. 507) confirms:

only = .76 (minimum)
NRRC = .96 and be annoyed = .96 (maximum, "close to ceiling")

Equations

Instances For

def TonhauserBeaverDegen2018.notAtIssuenessRating :

ExpressionType → ℚ

Mean not-at-issueness rating from Experiment 1a (0–1 scale). Measured via the "asking whether" diagnostic.

Higher = more not-at-issue (more backgrounded).

Values approximate means from Figure 3. Text (p. 508) confirms:

only = .73 (minimum)
NRRC = .96 (maximum)

Equations

Instances For

def TonhauserBeaverDegen2018.atIssuenessRating (e : ExpressionType) :

ℚ

At-issueness = 1 − not-at-issueness. Higher = more at-issue. Derived from the paper's direct measurements.

Equations

TonhauserBeaverDegen2018.atIssuenessRating e = 1 - TonhauserBeaverDegen2018.notAtIssuenessRating e

Instances For

inductive TonhauserBeaverDegen2018.Predicate :

The 12 clause-embedding predicates from Experiment 1b (p. 511).

Semantic classes (per paper):

Emotive: be amused, be annoyed
Cognitive: be aware, discover, find out, learn, notice, realize, establish
Sensory: see
Communication: confess, reveal

beAmused : Predicate
beAnnoyed : Predicate
beAware : Predicate
confess : Predicate
discover : Predicate
establish : Predicate
findOut : Predicate
learn : Predicate
notice : Predicate
realize : Predicate
reveal : Predicate
see : Predicate

Instances For

@[implicit_reducible]

instance TonhauserBeaverDegen2018.instDecidableEqPredicate :

DecidableEq Predicate

Equations

TonhauserBeaverDegen2018.instDecidableEqPredicate x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def TonhauserBeaverDegen2018.instReprPredicate.repr :

Predicate → ℕ → Std.Format

Equations

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

Instances For

@[implicit_reducible]

instance TonhauserBeaverDegen2018.instReprPredicate :

Equations

TonhauserBeaverDegen2018.instReprPredicate = { reprPrec := TonhauserBeaverDegen2018.instReprPredicate.repr }

def TonhauserBeaverDegen2018.verbProjectivity :

Predicate → ℚ

Mean projectivity ratings for the 12 predicates from Exp 1b (0–1 scale). Values approximate means from Figure 6.

Equations

Instances For

def TonhauserBeaverDegen2018.verbNotAtIssueness :

Predicate → ℚ

Mean not-at-issueness ratings for the 12 predicates from Exp 1b (0–1 scale). Values approximate means from Figure 6.

Equations

Instances For

def TonhauserBeaverDegen2018.verbAtIssueness (p : Predicate) :

ℚ

At-issueness = 1 − not-at-issueness for predicates.

Equations

TonhauserBeaverDegen2018.verbAtIssueness p = 1 - TonhauserBeaverDegen2018.verbNotAtIssueness p

Instances For

structure TonhauserBeaverDegen2018.RegressionEffect :

Regression coefficient: not-at-issueness predicts projectivity. Exp 1a (p. 508–509): β = 0.37, SE = 0.10, t = 3.70, p < .003. Exp 1b (p. 514): β = 0.34, SE = 0.04, t = 9.31, p < .0001.

The effect is significant in both experiments.

beta : ℚ
se : ℚ

Instances For

@[implicit_reducible]

instance TonhauserBeaverDegen2018.instReprRegressionEffect :

Repr RegressionEffect

Equations

TonhauserBeaverDegen2018.instReprRegressionEffect = { reprPrec := TonhauserBeaverDegen2018.instReprRegressionEffect.repr }

def TonhauserBeaverDegen2018.instReprRegressionEffect.repr :

RegressionEffect → ℕ → Std.Format

Equations

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

Instances For

def TonhauserBeaverDegen2018.exp1aRegression :

RegressionEffect

Equations

TonhauserBeaverDegen2018.exp1aRegression = { beta := 37 / 100, se := 10 / 100 }

Instances For

def TonhauserBeaverDegen2018.exp1bRegression :

RegressionEffect

Equations

TonhauserBeaverDegen2018.exp1bRegression = { beta := 34 / 100, se := 4 / 100 }

Instances For

structure TonhauserBeaverDegen2018.CorrelationData :

Pearson r for not-at-issueness × projectivity (positive correlation). "Collapsing" = computed over expression-type/predicate means. "Not collapsing" = computed over individual items.

Exp 1a (p. 508): r = .85 (collapsing), r = .45 (not collapsing) Exp 1b (p. 514): r = .99 (collapsing), r = .44 (not collapsing)

collapsing : ℚ
notCollapsing : ℚ

Instances For

@[implicit_reducible]

instance TonhauserBeaverDegen2018.instReprCorrelationData :

Repr CorrelationData

Equations

TonhauserBeaverDegen2018.instReprCorrelationData = { reprPrec := TonhauserBeaverDegen2018.instReprCorrelationData.repr }

def TonhauserBeaverDegen2018.instReprCorrelationData.repr :

CorrelationData → ℕ → Std.Format

Equations

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

Instances For

def TonhauserBeaverDegen2018.exp1aCorrelation :

CorrelationData

Equations

TonhauserBeaverDegen2018.exp1aCorrelation = { collapsing := 85 / 100, notCollapsing := 45 / 100 }

Instances For

def TonhauserBeaverDegen2018.exp1bCorrelation :

CorrelationData

Equations

TonhauserBeaverDegen2018.exp1bCorrelation = { collapsing := 99 / 100, notCollapsing := 44 / 100 }

Instances For

theorem TonhauserBeaverDegen2018.nrrc_annoyed_most_projective (e : ExpressionType) :

projectivityRating e ≤ projectivityRating ExpressionType.nrrc

NRRC and be annoyed are tied for most projective (text: .96).

theorem TonhauserBeaverDegen2018.only_least_projective (e : ExpressionType) :

projectivityRating ExpressionType.only ≤ projectivityRating e

only is the least projective at .76 (text confirms).

theorem TonhauserBeaverDegen2018.nrrc_most_notAtIssue (e : ExpressionType) :

notAtIssuenessRating e ≤ notAtIssuenessRating ExpressionType.nrrc

NRRC has the highest not-at-issueness at .96 (text confirms).

theorem TonhauserBeaverDegen2018.only_least_notAtIssue (e : ExpressionType) :

notAtIssuenessRating ExpressionType.only ≤ notAtIssuenessRating e

only has the lowest not-at-issueness at .73 (text confirms).

theorem TonhauserBeaverDegen2018.appositives_not_maximally_projective :

projectivityRating ExpressionType.nominalAppositive < 1

Appositives are not maximally projective, contra @cite{potts-2005}. Potts predicted CI content (including appositives) should project obligatorily. The data shows 94/100 — high but not 1.0.

theorem TonhauserBeaverDegen2018.within_type_variation :

projectivityRating ExpressionType.discover ≠ projectivityRating ExpressionType.know

Within-type variation: factive predicates differ in projectivity. discover (.88) vs know (.91) — both traditionally "factive" but different ratings.

theorem TonhauserBeaverDegen2018.gpp_extreme_pair_exp1a :

atIssuenessRating ExpressionType.only > atIssuenessRating ExpressionType.nrrc ∧ projectivityRating ExpressionType.only < projectivityRating ExpressionType.nrrc

GPP supported for Exp 1a extremes: only has highest at-issueness and lowest projectivity; NRRC has lowest at-issueness and highest projectivity.

theorem TonhauserBeaverDegen2018.beAnnoyed_highest_verb_projectivity (p : Predicate) :

verbProjectivity p ≤ verbProjectivity Predicate.beAnnoyed

be annoyed has the highest projectivity among the 12 predicates. (Tied with notice at .94.)

theorem TonhauserBeaverDegen2018.establish_lowest_verb_projectivity (p : Predicate) :

verbProjectivity Predicate.establish ≤ verbProjectivity p

establish has the lowest projectivity (.43) — notably below .50, suggesting it may not even be a projective trigger.

theorem TonhauserBeaverDegen2018.establish_below_midpoint :

verbProjectivity Predicate.establish < 1 / 2

establish is the only predicate with projectivity below the midpoint .50, suggesting it may not be a projective trigger.

theorem TonhauserBeaverDegen2018.gpp_extreme_pair_exp1b :

verbAtIssueness Predicate.establish > verbAtIssueness Predicate.beAnnoyed ∧ verbProjectivity Predicate.establish < verbProjectivity Predicate.beAnnoyed

GPP supported for Exp 1b extremes: establish has highest at-issueness and lowest projectivity.

theorem TonhauserBeaverDegen2018.non_establish_above_65 (p : Predicate) :

p ≠ Predicate.establish → 65 / 100 ≤ verbProjectivity p

All predicates except establish have projectivity ≥ .65.

theorem TonhauserBeaverDegen2018.exp1a_top_group_tight_range :

projectivityRating ExpressionType.nrrc - projectivityRating ExpressionType.know ≤ 6 / 100

The top group of Exp 1a (Table 1): {NRRC, annoyed, NomApp, possNP, know} show no significant pairwise differences in projectivity. These form the "high projectivity" cluster (.91–.96).

theorem TonhauserBeaverDegen2018.only_separated_from_top :

projectivityRating ExpressionType.nrrc - projectivityRating ExpressionType.only ≥ 15 / 100

only is significantly different from all other expression types (Table 1: all pairwise comparisons significant at p < .001).

theorem TonhauserBeaverDegen2018.exp1b_top_group_tight_range :

verbProjectivity Predicate.beAnnoyed - verbProjectivity Predicate.findOut ≤ 5 / 100

The top group of Exp 1b (Table 3): {annoyed, notice, aware, realize, amused, findOut} show no significant pairwise differences. These form the "high projectivity" cluster (.90–.94).

theorem TonhauserBeaverDegen2018.establish_separated_from_top :

verbProjectivity Predicate.beAnnoyed - verbProjectivity Predicate.establish ≥ 40 / 100

establish is clearly separated from the top group (Table 3: all pairwise comparisons significant at p < .001).

def TonhauserBeaverDegen2018.ExpressionType.toProjectivityDegree (e : ExpressionType) :

Core.Discourse.AtIssueness.ProjectivityDegree

Lift an expression type's projectivity rating to a bounded degree.

Equations

e.toProjectivityDegree = ⟨TonhauserBeaverDegen2018.projectivityRating e, ⋯⟩

Instances For

def TonhauserBeaverDegen2018.ExpressionType.toAtIssuenessDegree (e : ExpressionType) :

Core.Discourse.AtIssueness.AtIssuenessDegree

Lift an expression type's at-issueness to a bounded degree.

Equations

e.toAtIssuenessDegree = ⟨TonhauserBeaverDegen2018.atIssuenessRating e, ⋯⟩

Instances For

def TonhauserBeaverDegen2018.Predicate.toProjectivityDegree (p : Predicate) :

Core.Discourse.AtIssueness.ProjectivityDegree

Lift a predicate's projectivity rating to a bounded degree.

Equations

p.toProjectivityDegree = ⟨TonhauserBeaverDegen2018.verbProjectivity p, ⋯⟩

Instances For

def TonhauserBeaverDegen2018.Predicate.toAtIssuenessDegree (p : Predicate) :

Core.Discourse.AtIssueness.AtIssuenessDegree

Lift a predicate's at-issueness to a bounded degree.

Equations

p.toAtIssuenessDegree = ⟨TonhauserBeaverDegen2018.verbAtIssueness p, ⋯⟩

Instances For

def TonhauserBeaverDegen2018.classBMeanProjectivity :

ℚ

Mean projectivity for Class B triggers (NRRC, appositive, possessive NP).

Equations

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

Instances For

def TonhauserBeaverDegen2018.classCMeanProjectivity :

ℚ

Mean projectivity for Class C triggers (discover, know, annoyed, stop).

Equations

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

Instances For

theorem TonhauserBeaverDegen2018.classB_higher_projectivity_than_classC :

classCMeanProjectivity < classBMeanProjectivity

Class B triggers have higher mean projectivity than Class C triggers.

def TonhauserBeaverDegen2018.classBMeanNotAtIssueness :

ℚ

Mean not-at-issueness for Class B triggers.

Equations

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

Instances For

def TonhauserBeaverDegen2018.classCMeanNotAtIssueness :

ℚ

Mean not-at-issueness for Class C triggers.

Equations

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

Instances For

theorem TonhauserBeaverDegen2018.classB_higher_notAtIssueness_than_classC :

classCMeanNotAtIssueness < classBMeanNotAtIssueness

Class B triggers are more not-at-issue than Class C triggers.

theorem TonhauserBeaverDegen2018.all_expression_types_not_at_issue (e : ExpressionType) :

Core.Discourse.AtIssueness.toClassical e.toAtIssuenessDegree Core.Discourse.AtIssueness.defaultThreshold = Core.Discourse.AtIssueness.AtIssuenessClassical.notAtIssue

With the default threshold of 0.5, all 9 expression types are classified as not-at-issue.

theorem TonhauserBeaverDegen2018.establish_at_issue_default :

Core.Discourse.AtIssueness.toClassical Predicate.establish.toAtIssuenessDegree Core.Discourse.AtIssueness.defaultThreshold = Core.Discourse.AtIssueness.AtIssuenessClassical.atIssue

For Exp 1b predicates, only establish is classified as at-issue with the default threshold.

theorem TonhauserBeaverDegen2018.non_establish_not_at_issue (p : Predicate) (h : p ≠ Predicate.establish) :

Core.Discourse.AtIssueness.toClassical p.toAtIssuenessDegree Core.Discourse.AtIssueness.defaultThreshold = Core.Discourse.AtIssueness.AtIssuenessClassical.notAtIssue

All predicates except establish are classified as not-at-issue.

theorem TonhauserBeaverDegen2018.exp1b_gpp_antimonotone (p q : Predicate) :

verbAtIssueness p < verbAtIssueness q → verbProjectivity q ≤ verbProjectivity p

The GPP anti-monotonicity property holds for Exp 1b verb data.

theorem TonhauserBeaverDegen2018.exp1a_non_monotone_witness :

notAtIssuenessRating ExpressionType.possessiveNP > notAtIssuenessRating ExpressionType.nominalAppositive ∧ projectivityRating ExpressionType.possessiveNP < projectivityRating ExpressionType.nominalAppositive

Exp 1a is NOT fully anti-monotone: possNP and NomApp are non-monotone.

theorem TonhauserBeaverDegen2018.shared_predicates_gradient :

verbProjectivity Predicate.beAnnoyed > 1 / 2 ∧ verbProjectivity Predicate.discover > 1 / 2 ∧ verbProjectivity Predicate.reveal > 1 / 2 ∧ verbProjectivity Predicate.see > 1 / 2

Among shared predicates, discover shows intermediate at-issueness.

theorem TonhauserBeaverDegen2018.shared_predicates_intermediate_atissueness :

verbAtIssueness Predicate.discover > 0 ∧ verbAtIssueness Predicate.discover < 1 / 2 ∧ verbAtIssueness Predicate.beAnnoyed > 0 ∧ verbAtIssueness Predicate.beAnnoyed < 1 / 2