@cite{solstad-bott-2024} — Projectivity Bridge

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

Connects occasion verb presupposition to the @cite{tonhauser-beaver-roberts-simons-2013} taxonomy and formalizes the cataphoric resolution result from Experiment 3.

Key claims (S&P 17:11)

1. Occasion verbs trigger projective content (Exp 1): occasion verb content survives embedding under negation, questions, modals, and conditionals.
2. No strong contextual felicity (Exp 2): occasion verbs are felicitous "out of the blue" — their presupposition can be informative (accommodated).
3. Cataphoric resolution is possible (Exp 3): occasion verb presuppositions can be resolved by subsequent material (consequent of a conditional), supporting symmetric filtering over @cite{heim-1983}'s asymmetric left-to-right algorithm.

Tonhauser classification

These properties place occasion verbs in Class C (SCF=no, OLE=yes), alongside factive verbs (know) and change-of-state verbs (stop).

Symmetric vs asymmetric filtering

@cite{heim-1983}: local context at position i is computed from material to the LEFT of i only → presuppositions in the antecedent cannot be resolved by the consequent.

@cite{schlenker-2008}: local context considers material on BOTH sides → cataphoric resolution is predicted.

Solstad & Bott's Experiment 3 supports symmetric filtering: occasion verb presuppositions in the antecedent CAN be satisfied by the consequent.

theorem Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.occasion_verb_is_classC : Presupposition.ProjectiveContent.ProjectiveTrigger.occasion_verb.toClass = 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 Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.classC_no_scf : Presupposition.ProjectiveContent.ProjectiveClass.classC.scf = Presupposition.ProjectiveContent.StrongContextualFelicity.noRequires

Class C triggers do not require prior establishment in context.

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

Class C triggers have obligatory local effect under belief embedding.

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

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

def Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.occasionEventPhase {W : Type u_1} (occasion engagement outcome : W → Bool) : 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

• Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.occasionEventPhase occasion engagement outcome = { precondition := occasion, eventOccurs := engagement, consequence := outcome }

theorem Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.occasion_presup_projects {W : Type u_1} (occasion engagement outcome : W → Bool) : (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 Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.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 = false) : 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 Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.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

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

theorem Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.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 = true → trigger.presup w = true) : Semantics.Presupposition.LocalContext.presupFiltered (symmetricLocalCtxAntecedent c consequent) trigger

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

theorem Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.cataphoric_resolution_possible {W : Type u_1} (c : Semantics.Presupposition.LocalContext.LocalCtx W) (trigger consequent : Core.Presupposition.PrProp W) (h_entails : ∀ (w : W), c.worlds w → consequent.assertion w = true → trigger.presup w = true) : Semantics.Presupposition.LocalContext.presupFiltered (symmetricLocalCtxAntecedent c consequent) trigger

The key empirical finding: cataphoric resolution succeeds for occasion verbs (Exp 3, S&P 17:11). Participants accepted conditionals where:

• The antecedent contains an occasion verb (trigger)
• The consequent provides the occasion (resolver)

This is predicted by symmetric but NOT asymmetric filtering:

• Symmetric: consequent material available → presupposition filtered ✓
• Asymmetric: only left-to-right → presupposition projects ✗

The theorem shows that given a world model where the consequent entails the occasion, symmetric filtering correctly predicts the presupposition is filtered (matching experimental judgments).

theorem Phenomena.ImplicitCausality.Studies.SolstadBott2024.Projectivity.manage_projection_vs_implicature : Fragments.English.Predicates.Verbal.manage.implicativeBuilder = some Nadathur2024.Implicative.ImplicativeBuilder.positive ∧ Fragments.English.Predicates.Verbal.manage.presupType = some Core.Verbs.PresupTriggerType.prerequisiteSoft ∧ Fragments.English.Predicates.Verbal.manage_occasion.implicativeBuilder = some Nadathur2024.Implicative.ImplicativeBuilder.positive ∧ Fragments.English.Predicates.Verbal.manage_occasion.presupType = some Core.Verbs.PresupTriggerType.prerequisiteSoft

The occasion presupposition (projective content) is distinct from the implicative inference (at-issue content). For "manage to VP":

• Implicative inference: VP occurred (at-issue, cancels under negation) "John didn't manage to open the door" → door was NOT opened
• Occasion presupposition: opening was difficult (projective, survives negation) "John didn't manage to open the door" → opening WAS difficult

Both manage and manage_occasion have prerequisite presuppositions (@cite{nadathur-2024} Proposal 32i); the occasion sense additionally has a context-specific prerequisite.