Solstad & Bott (2024): The occasion verb presupposition

@cite{solstad-bott-2024} @cite{tonhauser-beaver-roberts-simons-2013} @cite{heim-1983} @cite{schlenker-2008} @cite{schlenker-2009}

Formalizes the experimental evidence from S&P 17:11 establishing occasion verbs as a distinct class of presupposition trigger.

The occasion verb presupposition

Occasion verbs (German: bestrafen "punish", kritisieren "criticise", loben "praise", danken "thank", ...) are interpersonal action verbs whose agent performs an action in response to a prior eventuality involving the object. This prior eventuality — the occasion — is presupposed.

Example: "The judge punished Peter"

• At-issue: the judge performed a punishing action
• Presupposed: Peter did something wrong (the occasion)

Experimental evidence (3 experiments)

Exp 1 (occasion verbs only, N=71):

• Block 1 (contextual felicity): occasion verbs are rated better in anaphoric (β=22.37) and cataphoric (β=17.95) than neutral contexts. Cataphoric resolution is unique to occasion verbs — pronouns and demonstratives show NO cataphoric improvement.
• Block 2 (projectivity/at-issueness): mean projectivity 0.79 (range 0.73–0.87), mean at-issueness 0.32 (range 0.17–0.57).

Exp 2 (occasion + SE + ES psych verbs, N=60):

• Block 2: occasion verbs (0.69 proj) separate from SE (0.54) and ES (0.52). k-means k=3 separates {occasion} from {psych verbs}. H6 (SE = occasion) REJECTED; H7 (ES ≠ occasion) CONFIRMED.

Exp 3 (filtering, N=58):

• Occasion verbs: trigger-first and trigger-last NOT significantly different (β=−1.97, t=−1.05) → symmetric filtering.
• Mandelkern items (factives/aspectuals): trigger-first >> trigger-last (β=−30.16, t=−16.33) → asymmetric filtering.

Tonhauser et al. (2013) classification

Occasion verbs are Class C (SCF=no, OLE=yes), alongside factives (know) and change-of-state verbs (stop). However, they are distinguished by their bidirectional context resolution (both m-anaphoric and m-cataphoric) and symmetric filtering — they constitute "a cage of their own" within the trigger taxonomy.

inductive SolstadBott2024.FilteringDirection : Type

Filtering direction for presupposition triggers. @cite{solstad-bott-2024} Exp 3 shows occasion verbs allow symmetric filtering, while factives and change-of-state verbs only allow left-to-right filtering.

• leftToRight : FilteringDirection
• symmetric : FilteringDirection

@[implicit_reducible]

instance SolstadBott2024.instDecidableEqFilteringDirection : DecidableEq FilteringDirection

Equations

• SolstadBott2024.instDecidableEqFilteringDirection x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def SolstadBott2024.instReprFilteringDirection.repr : FilteringDirection → ℕ → Std.Format

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

@[implicit_reducible]

instance SolstadBott2024.instReprFilteringDirection : Repr FilteringDirection

Equations

• SolstadBott2024.instReprFilteringDirection = { reprPrec := SolstadBott2024.instReprFilteringDirection.repr }

inductive SolstadBott2024.ContextPolarity : Type

Context resolution direction for presupposition triggers. Refines @cite{tonhauser-beaver-roberts-simons-2013}'s "m-positive" into finer-grained categories based on where the resolving material can appear.

• mNeutral : ContextPolarity
• mAnaphoric : ContextPolarity
• mCataphoric : ContextPolarity

@[implicit_reducible]

instance SolstadBott2024.instDecidableEqContextPolarity : DecidableEq ContextPolarity

Equations

• SolstadBott2024.instDecidableEqContextPolarity x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance SolstadBott2024.instReprContextPolarity : Repr ContextPolarity

Equations

• SolstadBott2024.instReprContextPolarity = { reprPrec := SolstadBott2024.instReprContextPolarity.repr }

def SolstadBott2024.instReprContextPolarity.repr : ContextPolarity → ℕ → Std.Format

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

theorem SolstadBott2024.occasion_verb_is_classC : Phenomena.Presupposition.ProjectiveContent.ProjectiveTrigger.occasion_verb.toClass = Phenomena.Presupposition.ProjectiveContent.ProjectiveClass.classC

Occasion verbs are Class C in the @cite{tonhauser-beaver-roberts-simons-2013} taxonomy: SCF=no (can be informative), OLE=yes (attributed to attitude holder).

theorem SolstadBott2024.classC_no_scf : Phenomena.Presupposition.ProjectiveContent.ProjectiveClass.classC.scf = Phenomena.Presupposition.ProjectiveContent.StrongContextualFelicity.noRequires

Class C triggers do not require prior establishment in context.

theorem SolstadBott2024.classC_has_ole : Phenomena.Presupposition.ProjectiveContent.ProjectiveClass.classC.ole = Phenomena.Presupposition.ProjectiveContent.ObligatoryLocalEffect.obligatory

Class C triggers have obligatory local effect under belief embedding.

theorem SolstadBott2024.occasion_verb_patterns_with_stop_know : Phenomena.Presupposition.ProjectiveContent.ProjectiveTrigger.occasion_verb.toClass = Phenomena.Presupposition.ProjectiveContent.ProjectiveTrigger.stop_prestate.toClass ∧ Phenomena.Presupposition.ProjectiveContent.ProjectiveTrigger.occasion_verb.toClass = Phenomena.Presupposition.ProjectiveContent.ProjectiveTrigger.know_complement.toClass

Occasion verbs pattern with stop and know — all Class C.

def SolstadBott2024.occasionVerbEntries : List Fragments.German.Predicates.GermanVerbEntry

The 16 German occasion verbs tested in @cite{solstad-bott-2024}, derived from Fragment entries with .occasion sense tag.

Equations

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theorem SolstadBott2024.occasion_verb_count : occasionVerbEntries.length = 16

16 occasion verbs were tested.

theorem SolstadBott2024.all_occasion_entries_tagged : (occasionVerbEntries.all fun (x : Fragments.German.Predicates.GermanVerbEntry) => x.senseTag == Semantics.Lexical.SenseTag.occasion) = true

All entries in the occasion verb list use the .occasion sense tag.

theorem SolstadBott2024.all_occasion_entries_soft_trigger : (occasionVerbEntries.all fun (x : Fragments.German.Predicates.GermanVerbEntry) => x.presupType == some Semantics.Lexical.PresupTriggerType.softTrigger) = true

All entries in the occasion verb list are soft presupposition triggers.

structure SolstadBott2024.Exp1Regression : Type

Exp 1 Block 1 regression estimates (Table 1 of @cite{solstad-bott-2024}). Intercept = occasion verb in neutral context. Other coefficients are treatment contrasts. N=71 participants (16 occasion verbs × 3 context conditions).

• intercept : ℚ

  Intercept: occasion verb, neutral context (0–100 scale)

• neutral_to_anaphoric : ℚ

  Neutral → anaphoric improvement (occasion verbs)

• neutral_to_cataphoric : ℚ

  Neutral → cataphoric improvement (occasion verbs)

def SolstadBott2024.instReprExp1Regression.repr : Exp1Regression → ℕ → Std.Format

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@[implicit_reducible]

instance SolstadBott2024.instReprExp1Regression : Repr Exp1Regression

Equations

• SolstadBott2024.instReprExp1Regression = { reprPrec := SolstadBott2024.instReprExp1Regression.repr }

def SolstadBott2024.exp1_regression : Exp1Regression

Exp 1, Table 1 fixed effects.

Equations

• SolstadBott2024.exp1_regression = { intercept := 5081 / 100, neutral_to_anaphoric := 2237 / 100, neutral_to_cataphoric := 1795 / 100 }

theorem SolstadBott2024.occasion_verb_bidirectional_resolution : exp1_regression.neutral_to_anaphoric > 0 ∧ exp1_regression.neutral_to_cataphoric > 0

Occasion verbs improve in both anaphoric AND cataphoric contexts. This bidirectional improvement is unique to occasion verbs — pronouns and demonstratives show no cataphoric improvement.

theorem SolstadBott2024.cataphoric_resolution_substantial : exp1_regression.neutral_to_cataphoric > 10

The cataphoric improvement is substantial (>10 points on 0–100 scale), not a marginal effect.

structure SolstadBott2024.ProjectivityDatum : Type

Exp 1 Block 2: projectivity and at-issueness ratings (0–1 scale). Gradient measures following @cite{tonhauser-beaver-degen-2018}.

• projectivity : ℚ
• atIssueness : ℚ
• projLow : ℚ
• projHigh : ℚ

def SolstadBott2024.instReprProjectivityDatum.repr : ProjectivityDatum → ℕ → Std.Format

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@[implicit_reducible]

instance SolstadBott2024.instReprProjectivityDatum : Repr ProjectivityDatum

Equations

• SolstadBott2024.instReprProjectivityDatum = { reprPrec := SolstadBott2024.instReprProjectivityDatum.repr }

def SolstadBott2024.exp1_occasion_proj : ProjectivityDatum

Occasion verb projectivity/at-issueness from Exp 1 Block 2.

Equations

• SolstadBott2024.exp1_occasion_proj = { projectivity := 79 / 100, atIssueness := 32 / 100, projLow := 73 / 100, projHigh := 87 / 100 }

theorem SolstadBott2024.exp1_high_projectivity : exp1_occasion_proj.projectivity ≥ 70 / 100

Occasion verbs have high projectivity (≥ 0.70).

theorem SolstadBott2024.exp1_not_at_issue : exp1_occasion_proj.atIssueness < 50 / 100

Occasion verb content is not at-issue (at-issueness < 0.50).

def SolstadBott2024.exp2VerbClasses : List SolstadBott2022.VerbClass

Exp 2 verb classes correspond to @cite{solstad-bott-2022} verb classes. Occasion verbs = agent-evocator, SE = stimulus-experiencer, ES = experiencer-stimulus.

Equations

• SolstadBott2024.exp2VerbClasses = [SolstadBott2022.VerbClass.agentEvocator, SolstadBott2022.VerbClass.stimExp, SolstadBott2022.VerbClass.expStim]

structure SolstadBott2024.Exp2ProjectivityDatum : Type

Exp 2 Block 2: projectivity by verb class. N=60 participants. 16 occasion verbs, 9 SE verbs, 9 ES verbs. The key finding: psych verbs have LOWER projectivity than occasion verbs, and k-means k=3 clustering separates them.

• verbClass : SolstadBott2022.VerbClass
• projectivity : ℚ
• atIssueness : ℚ

@[implicit_reducible]

instance SolstadBott2024.instReprExp2ProjectivityDatum : Repr Exp2ProjectivityDatum

Equations

• SolstadBott2024.instReprExp2ProjectivityDatum = { reprPrec := SolstadBott2024.instReprExp2ProjectivityDatum.repr }

def SolstadBott2024.instReprExp2ProjectivityDatum.repr : Exp2ProjectivityDatum → ℕ → Std.Format

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def SolstadBott2024.exp2_occasion_proj : Exp2ProjectivityDatum

Equations

• SolstadBott2024.exp2_occasion_proj = { verbClass := SolstadBott2022.VerbClass.agentEvocator, projectivity := 69 / 100, atIssueness := 35 / 100 }

def SolstadBott2024.exp2_stimExp_proj : Exp2ProjectivityDatum

Equations

• SolstadBott2024.exp2_stimExp_proj = { verbClass := SolstadBott2022.VerbClass.stimExp, projectivity := 54 / 100, atIssueness := 52 / 100 }

def SolstadBott2024.exp2_expStim_proj : Exp2ProjectivityDatum

Equations

• SolstadBott2024.exp2_expStim_proj = { verbClass := SolstadBott2022.VerbClass.expStim, projectivity := 52 / 100, atIssueness := 46 / 100 }

theorem SolstadBott2024.h6_rejected_se_not_occasion : exp2_occasion_proj.projectivity > exp2_stimExp_proj.projectivity

H6 REJECTED: If the occasion implication were shared by all IC verbs, we would expect SE verbs to pattern with occasion verbs. They do not: occasion verbs (0.69) >> SE verbs (0.54).

theorem SolstadBott2024.h7_confirmed_es_not_occasion : exp2_occasion_proj.projectivity > exp2_expStim_proj.projectivity

H7 CONFIRMED: ES verbs do not cluster with occasion verbs either. Occasion verbs (0.69) >> ES verbs (0.52).

theorem SolstadBott2024.psych_verbs_cluster_together : exp2_occasion_proj.projectivity - exp2_stimExp_proj.projectivity > exp2_stimExp_proj.projectivity - exp2_expStim_proj.projectivity

SE and ES psych verbs cluster together rather than with occasion verbs: the gap between occasion and SE (0.15) >> gap between SE and ES (0.02).

inductive SolstadBott2024.TriggerPosition : Type

Trigger position conditions in Exp 3 (filtering experiment). Items are conjunctions in the antecedent of a conditional.

• triggerFirst : TriggerPosition
• triggerLast : TriggerPosition
• triggerOnly : TriggerPosition

@[implicit_reducible]

instance SolstadBott2024.instDecidableEqTriggerPosition : DecidableEq TriggerPosition

Equations

• SolstadBott2024.instDecidableEqTriggerPosition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def SolstadBott2024.instReprTriggerPosition.repr : TriggerPosition → ℕ → Std.Format

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@[implicit_reducible]

instance SolstadBott2024.instReprTriggerPosition : Repr TriggerPosition

Equations

• SolstadBott2024.instReprTriggerPosition = { reprPrec := SolstadBott2024.instReprTriggerPosition.repr }

inductive SolstadBott2024.Exp3TriggerClass : Type

Trigger class conditions in Exp 3. Separate regression analyses were run for each class.

• occasionVerb : Exp3TriggerClass
• mandelkern : Exp3TriggerClass

@[implicit_reducible]

instance SolstadBott2024.instDecidableEqExp3TriggerClass : DecidableEq Exp3TriggerClass

Equations

• SolstadBott2024.instDecidableEqExp3TriggerClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def SolstadBott2024.instReprExp3TriggerClass.repr : Exp3TriggerClass → ℕ → Std.Format

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@[implicit_reducible]

instance SolstadBott2024.instReprExp3TriggerClass : Repr Exp3TriggerClass

Equations

• SolstadBott2024.instReprExp3TriggerClass = { reprPrec := SolstadBott2024.instReprExp3TriggerClass.repr }

structure SolstadBott2024.Exp3RegressionDatum : Type

Exp 3 regression results from Table 3 of @cite{solstad-bott-2024}. N=58 (75 recruited, 17 excluded). Fixed-effect estimates from mixed-effects regression; reference level is trigger-first.

• triggerClass : Exp3TriggerClass
• intercept : ℚ

  Intercept (trigger-first condition, the reference level)

• trigOnly_vs_trigFirst : ℚ

  Contrast: trigger-only minus trigger-first

• trigLast_vs_trigFirst : ℚ

  Contrast: trigger-last minus trigger-first (KEY test for symmetry)

• tValue : ℚ

  t-value for the trigger-last vs trigger-first contrast

def SolstadBott2024.instReprExp3RegressionDatum.repr : Exp3RegressionDatum → ℕ → Std.Format

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@[implicit_reducible]

instance SolstadBott2024.instReprExp3RegressionDatum : Repr Exp3RegressionDatum

Equations

• SolstadBott2024.instReprExp3RegressionDatum = { reprPrec := SolstadBott2024.instReprExp3RegressionDatum.repr }

def SolstadBott2024.exp3_occasion : Exp3RegressionDatum

Analysis B: occasion verb filtering. Trigger-first ≈ trigger-last.

Equations

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

def SolstadBott2024.exp3_mandelkern : Exp3RegressionDatum

Analysis C: Mandelkern items (factives/aspectuals). Trigger-first << trigger-last.

Equations

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

theorem SolstadBott2024.exp3_occasion_symmetric : exp3_occasion.trigLast_vs_trigFirst > -5 ∧ exp3_occasion.trigLast_vs_trigFirst < 5 ∧ exp3_occasion.tValue > -2 ∧ exp3_occasion.tValue < 2

SYMMETRIC FILTERING for occasion verbs: trigger-first ≈ trigger-last. The estimate (−1.97) is small and not statistically significant (|t| = 1.05 < 2). Occasion verbs filter equally well regardless of whether the resolver precedes or follows the trigger.

theorem SolstadBott2024.exp3_mandelkern_asymmetric : exp3_mandelkern.trigLast_vs_trigFirst < -20 ∧ exp3_mandelkern.tValue < -10

ASYMMETRIC FILTERING for Mandelkern items (factives/aspectuals): trigger-first << trigger-last. The estimate (−30.16) is large and highly significant (|t| = 16.33 >> 2). These triggers filter much better when the resolver precedes the trigger (left-to-right only).

theorem SolstadBott2024.filtering_distinguishes_trigger_classes : exp3_mandelkern.trigLast_vs_trigFirst < 10 * exp3_occasion.trigLast_vs_trigFirst

The filtering asymmetry distinguishes occasion verbs from factives/ aspectuals — the Mandelkern effect is >10× larger.

theorem SolstadBott2024.h8_interaction : exp3_occasion.trigOnly_vs_trigFirst > 10 ∧ exp3_mandelkern.trigOnly_vs_trigFirst > 0 ∧ exp3_occasion.trigLast_vs_trigFirst > -5 ∧ exp3_mandelkern.trigLast_vs_trigFirst < -20

H8 (interaction hypothesis): occasion verbs pattern with factives/ aspectuals for left-to-right filtering (both show the trigger-only vs trigger-last contrast), but differ qualitatively for right-to-left filtering (trigger-first condition). Occasion verbs: trigger-first ≈ trigger-last. Factives/aspectuals: trigger-first >> trigger-last.

structure SolstadBott2024.TriggerProfile : Type

Profile characterizing a presupposition trigger's behavior across the dimensions tested by @cite{solstad-bott-2024}. Uses types from the library's projective content taxonomy and the filtering/polarity types defined in this file.

• projectiveClass : Phenomena.Presupposition.ProjectiveContent.ProjectiveClass
• contextPolarities : List ContextPolarity
• filteringDirection : FilteringDirection

def SolstadBott2024.instDecidableEqTriggerProfile.decEq (x✝ x✝¹ : TriggerProfile) : Decidable (x✝ = x✝¹)

Equations

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

@[implicit_reducible]

instance SolstadBott2024.instDecidableEqTriggerProfile : DecidableEq TriggerProfile

Equations

• SolstadBott2024.instDecidableEqTriggerProfile = SolstadBott2024.instDecidableEqTriggerProfile.decEq

@[implicit_reducible]

instance SolstadBott2024.instReprTriggerProfile : Repr TriggerProfile

Equations

• SolstadBott2024.instReprTriggerProfile = { reprPrec := SolstadBott2024.instReprTriggerProfile.repr }

def SolstadBott2024.instReprTriggerProfile.repr : TriggerProfile → ℕ → Std.Format

Equations

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

def SolstadBott2024.occasionVerbProfile : TriggerProfile

Occasion verb trigger profile: Class C, bidirectional resolution, symmetric filtering.

Equations

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

def SolstadBott2024.factiveProfile : TriggerProfile

Factive/aspectual trigger profile: Class C, no SCF constraint (neutral ≈ anaphoric in Exp 1 data), left-to-right filtering.

Equations

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

theorem SolstadBott2024.same_projective_class : occasionVerbProfile.projectiveClass = factiveProfile.projectiveClass

Occasion verbs share Class C with factives.

theorem SolstadBott2024.cage_of_their_own : occasionVerbProfile ≠ factiveProfile

Despite sharing Class C, occasion verbs differ from factives in both context resolution and filtering — the "cage of their own" result.

theorem SolstadBott2024.distinguished_by_filtering_not_class : occasionVerbProfile.filteringDirection ≠ factiveProfile.filteringDirection ∧ occasionVerbProfile.contextPolarities ≠ factiveProfile.contextPolarities

The distinguishing features are filtering direction and bidirectionality, not the projective class assignment.

def SolstadBott2024.occasionEventPhase {W : Type u_1} (occasion engagement outcome : W → Prop) : Semantics.Presupposition.OntologicalPreconditions.EventPhase W

Model an occasion verb's presupposition as an EventPhase.

Example: "The judge punished Peter"

• precondition = Peter did something wrong (the occasion)
• eventOccurs = the judge's punishing action
• consequence = Peter is punished

The precondition (occasion) is what projects.

Equations

• SolstadBott2024.occasionEventPhase occasion engagement outcome = { precondition := occasion, eventOccurs := engagement, consequence := outcome }

theorem SolstadBott2024.occasion_presup_projects {W : Type u_1} (occasion engagement outcome : W → Prop) : (Semantics.Presupposition.OntologicalPreconditions.affirmative (occasionEventPhase occasion engagement outcome)).presupposition = (Semantics.Presupposition.OntologicalPreconditions.negative (occasionEventPhase occasion engagement outcome)).presupposition

Occasion presupposition projects through negation. "The judge didn't punish Peter" still presupposes Peter did something wrong.

theorem SolstadBott2024.heim_antecedent_projects {W : Type u_1} (c : Core.CommonGround.ContextSet W) (trigger _consequence : Core.Presupposition.PrProp W) (h : ∃ (w : W), c w ∧ ¬trigger.presup w) : Semantics.Presupposition.LocalContext.presupProjects (Semantics.Presupposition.LocalContext.initialLocalCtx c) trigger

Under Heim's asymmetric filtering, the local context at the antecedent of a conditional is just the global context — no material from the consequent is available. So if the occasion verb is in the antecedent, its presupposition PROJECTS (is not filtered).

"If the judge punishes Peter, he was convicted." At "punishes" (antecedent): local context = global context. Presupposition "Peter did something wrong" is NOT entailed → projects.

def SolstadBott2024.symmetricLocalCtxAntecedent {W : Type u_1} (c : Semantics.Presupposition.LocalContext.LocalCtx W) (consequent : Core.Presupposition.PrProp W) : Semantics.Presupposition.LocalContext.LocalCtx W

Under symmetric filtering, material from the consequent IS available to resolve presuppositions in the antecedent. We model this by providing the consequent's assertion to the local context at the antecedent position.

"If the judge punishes Peter, he was convicted." Symmetric local context at "punishes": c + [Peter was convicted]. Presupposition "Peter did something wrong" IS entailed → filtered.

Equations

• SolstadBott2024.symmetricLocalCtxAntecedent c consequent = { worlds := c.worlds.update consequent.assertion, position := c.position, depth := c.depth }

theorem SolstadBott2024.symmetric_filters_when_consequent_entails {W : Type u_1} (c : Semantics.Presupposition.LocalContext.LocalCtx W) (trigger consequent : Core.Presupposition.PrProp W) (h : ∀ (w : W), c.worlds w → consequent.assertion w → trigger.presup w) : Semantics.Presupposition.LocalContext.presupFiltered (symmetricLocalCtxAntecedent c consequent) trigger

When the consequent entails the occasion presupposition, symmetric filtering predicts the presupposition is filtered.

theorem SolstadBott2024.occasion_is_agent_evocator_bias : SolstadBott2022.VerbClass.agentEvocator.predictedBias = SolstadBott2022.ICBias.np2

Occasion verbs correspond to the agent-evocator class from @cite{solstad-bott-2022}. The "occasion" presupposition is the same underspecified eventuality that drives the NP2 IC bias: the evocator's prior behavior triggers the agent's interpersonal response.

theorem SolstadBott2024.ic_and_presupposition_dissociate : SolstadBott2022.VerbClass.agentEvocator.predictedBias = SolstadBott2022.VerbClass.expStim.predictedBias ∧ exp2_occasion_proj.projectivity > exp2_stimExp_proj.projectivity ∧ exp2_occasion_proj.projectivity > exp2_expStim_proj.projectivity

Despite sharing IC properties with psych verbs, occasion verbs have higher projectivity (Exp 2). The IC bias and the presupposition are distinct phenomena: IC bias tracks which argument is explained in "because" continuations, while the presupposition is a projective content that survives embedding under negation, questions, and modals.

def SolstadBott2024.exp1_occasion_gpp : Core.Discourse.AtIssueness.GradientPair

Occasion verb projectivity/at-issueness from Exp 1 as a GradientPair, bridging to the @cite{tonhauser-beaver-degen-2018} infrastructure.

Equations

• SolstadBott2024.exp1_occasion_gpp = { atIssueness := SolstadBott2024.exp1_occasion_proj.atIssueness, projectivity := SolstadBott2024.exp1_occasion_proj.projectivity }

def SolstadBott2024.exp2_occasion_gpp : Core.Discourse.AtIssueness.GradientPair

Occasion verb GradientPair from Exp 2.

Equations

• SolstadBott2024.exp2_occasion_gpp = { atIssueness := SolstadBott2024.exp2_occasion_proj.atIssueness, projectivity := SolstadBott2024.exp2_occasion_proj.projectivity }

def SolstadBott2024.exp2_stimExp_gpp : Core.Discourse.AtIssueness.GradientPair

SE psych verb GradientPair from Exp 2.

Equations

• SolstadBott2024.exp2_stimExp_gpp = { atIssueness := SolstadBott2024.exp2_stimExp_proj.atIssueness, projectivity := SolstadBott2024.exp2_stimExp_proj.projectivity }

def SolstadBott2024.exp2_expStim_gpp : Core.Discourse.AtIssueness.GradientPair

ES psych verb GradientPair from Exp 2.

Equations

• SolstadBott2024.exp2_expStim_gpp = { atIssueness := SolstadBott2024.exp2_expStim_proj.atIssueness, projectivity := SolstadBott2024.exp2_expStim_proj.projectivity }

def SolstadBott2024.exp1_gpp_r : ℚ

Pearson r for the correlation between at-issueness and projectivity, aggregated over trigger types.

Exp 1 (8 trigger types including occasion verbs): r = −0.70, t(6) = −2.37, p = .06 (marginally significant)

Exp 2 (9 trigger types including occasion + psych verbs): r = −0.90, t(7) = −5.33, p < .01 (significant)

These correspond to @cite{tonhauser-beaver-degen-2018}'s positive correlations between not-at-issueness and projectivity (r = .85, .99), since at-issueness = 1 − not-at-issueness flips the sign.

Equations

• SolstadBott2024.exp1_gpp_r = -70 / 100

def SolstadBott2024.exp2_gpp_r : ℚ

Equations

• SolstadBott2024.exp2_gpp_r = -90 / 100

theorem SolstadBott2024.exp2_gpp_stronger : exp2_gpp_r < exp1_gpp_r

The GPP anti-correlation strengthens from Exp 1 to Exp 2, with more trigger types included.

theorem SolstadBott2024.occasion_verbs_satisfy_gpp : exp1_occasion_gpp.projectivity > 1 / 2 ∧ exp1_occasion_gpp.atIssueness < 1 / 2 ∧ exp2_occasion_gpp.projectivity > 1 / 2 ∧ exp2_occasion_gpp.atIssueness < 1 / 2

Occasion verbs satisfy the GPP: high projectivity paired with low at-issueness in both experiments.

theorem SolstadBott2024.psych_verbs_midrange : exp2_stimExp_gpp.projectivity > 40 / 100 ∧ exp2_stimExp_gpp.projectivity < 60 / 100 ∧ exp2_stimExp_gpp.atIssueness > 40 / 100 ∧ exp2_stimExp_gpp.atIssueness < 60 / 100

Psych verbs are mid-range on both dimensions: neither clearly projective nor clearly at-issue, placing them outside the GPP pattern that occasion verbs and other triggers follow.

theorem SolstadBott2024.gpp_orders_occasion_vs_psych : exp2_occasion_gpp.projectivity > exp2_stimExp_gpp.projectivity ∧ exp2_occasion_gpp.atIssueness < exp2_stimExp_gpp.atIssueness ∧ exp2_occasion_gpp.projectivity > exp2_expStim_gpp.projectivity ∧ exp2_occasion_gpp.atIssueness < exp2_expStim_gpp.atIssueness

The GPP orders occasion verbs and psych verbs correctly: occasion verbs have higher projectivity AND lower at-issueness.