An event decomposed into temporal phases:
- Precondition: State that must hold BEFORE for the event to be possible
- The event occurrence itself
- Consequence: State that holds AFTER the event
- precondition : W → Bool
Precondition: must hold before the event for it to be possible
- eventOccurs : W → Bool
The event actually occurs
- consequence : W → Bool
Consequence: holds after the event (result state)
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Well-formed event: precondition enables the event.
This is the ontological constraint: you can't stop smoking unless you were smoking.
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- e.wellFormed = ∀ (w : W), e.eventOccurs w = true → e.precondition w = true
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"Stop P" as an event phase
Equations
- Semantics.Presupposition.OntologicalPreconditions.stopAsEventPhase P = { precondition := P, eventOccurs := P, consequence := fun (w : W) => !P w }
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"Start P" as an event phase
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"Continue P" as an event phase
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- Semantics.Presupposition.OntologicalPreconditions.continueAsEventPhase P = { precondition := P, eventOccurs := P, consequence := P }
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Event phase precondition = CoS presupposition.
Event phase consequence = CoS assertion.
A sentence that refers to an event type and makes a claim about it.
The event type referenced is independent of the claim made. Both affirmative and negative sentences can refer to the same event type.
- eventType : EventPhase W
The event type this sentence is about
- polarity : Core.Polarity
The polarity of the claim
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The "aboutness" of a sentence: what event type it refers to.
This is independent of polarity: both "John stopped" and "John didn't stop" are about the same event type (the stopping).
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The assertion made by a sentence depends on polarity.
- Affirmed: The event occurred (consequence holds)
- Negated: The event didn't occur (consequence doesn't hold)
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The presupposition comes from aboutness, not from the assertion.
Presuppositions are tied to event reference, not to the claim being made.
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Construct an affirmative sentence about an event type.
Equations
- Semantics.Presupposition.OntologicalPreconditions.affirmative e = { eventType := e, polarity := Core.Polarity.positive }
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Construct a negative sentence about an event type.
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- Semantics.Presupposition.OntologicalPreconditions.negative e = { eventType := e, polarity := Core.Polarity.negative }
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Affirmative and negative sentences have the same aboutness.
Both "John stopped smoking" and "John didn't stop smoking" are about the same event type, the stopping event. This is the structural basis for presupposition projection.
Presuppositions project because they come from shared aboutness.
Since presuppositions are derived from aboutness, and aboutness is shared across polarities, presuppositions must be shared too.
Assertions differ by polarity.
While presuppositions are shared, assertions differ: the negative asserts the opposite of the affirmative.
Presupposition is independent of assertion content.
The presupposition depends only on the event type, not on what is asserted. This is what makes presuppositions "backgrounded": they're part of what we're talking about, not what we're saying about it.
Under the assertion-only view, we just have truth conditions.
- truthConditions : W → Bool
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Under assertion-only, "stop P" just means: was P and now ¬P.
Without temporal indices, this collapses to P w ∧ ¬P w at a single
world — always false. This demonstrates that purely extensional
(single-index) semantics cannot represent CoS verbs: the pre-state
and post-state refer to different temporal indices, and flattening
them into one evaluation point produces a contradiction.
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Under assertion-only, "not stop P" just means: ¬(was P and now ¬P).
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Under assertion-only, the negation does not entail the precondition.
The negated assertion !(P w && !P w) = !P w ∨ P w is true when P w is false. So we cannot infer P from the negated sentence.
This demonstrates the inadequacy of the assertion-only view: it cannot explain why "John didn't stop smoking" presupposes he was smoking.
Under the aboutness view, both sentences refer to the stopping event. The stopping event has precondition P (was smoking). Therefore, both sentences presuppose P.
For "stop P", both affirmative and negative presuppose P.
This is the core empirical prediction that the aboutness view explains and the assertion-only view cannot.
Consequential event: the event entails its consequence when it occurs.
Equations
- e.hasConsequence = ∀ (w : W), e.eventOccurs w = true → e.consequence w = true
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Consequences do not project through negation.
Under "not E", the event didn't occur, so we can't infer the consequence. This explains why "John didn't stop smoking" doesn't entail he's not smoking.
The asymmetry:
- Preconditions: tied to event reference, so they project
- Consequences: tied to event occurrence, so they don't project under negation
Structural explanation: why preconditions project and consequences don't.
- Presupposition = aboutness.precondition (comes from event reference)
- Assertion = depends on polarity (comes from claim about occurrence)
- Consequence = entailed by occurrence (part of assertion, not aboutness)
Under negation:
- Event reference is preserved → presupposition preserved
- Occurrence is denied → consequence not entailed
Assertions differ at any world where the consequence is definite (true or false).
If the consequence is true at w, affirmative says true and negative says false. If the consequence is false at w, affirmative says false and negative says true.
Presuppositions are constant across polarity; assertions vary with polarity.
Presuppositions are tied to event reference (which is constant), not to the claim (which varies).
The precondition/consequence asymmetry under negation.
Under negation, precondition content survives (via presupposition) but consequence content is denied (via assertion). This is the structural basis for why preconditions are the default accommodation target (@cite{roberts-simons-2024} p. 721): accommodating preconditions is consistent with both affirming and denying the event, while accommodating consequences is only consistent with affirmation.
The converse: under affirmation, precondition survives AND consequence is asserted. Preconditions are consistent with BOTH polarities; consequences are consistent with only one.
An event is telic if its consequence differs from its precondition.
This is the existential property: there exists some world where precondition ≠ consequence, indicating a state change.
Equations
- e.isTelic = ∃ (w : W), e.precondition w ≠ e.consequence w
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An event is atelic if precondition and consequence are the same.
This is the universal property: in all worlds, the state persists.
Equations
- e.isAtelic = ∀ (w : W), e.precondition w = e.consequence w
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"Stop P" is telic: state changes from P to ¬P
"Continue P" is atelic: no state change
"Start P" is telic: state changes from ¬P to P
Aspectual profile for CoS verb types.
- "stop": Achievement profile (telic, punctual change to ¬P)
- "start": Achievement profile (telic, punctual change to P)
- "continue": Activity profile (atelic, durative persistence)
Equations
- Semantics.Presupposition.OntologicalPreconditions.cosTypeToAspectualProfile Semantics.Lexical.Verb.ChangeOfState.CoSType.cessation = Semantics.Tense.Aspect.LexicalAspect.achievementProfile
- Semantics.Presupposition.OntologicalPreconditions.cosTypeToAspectualProfile Semantics.Lexical.Verb.ChangeOfState.CoSType.inception = Semantics.Tense.Aspect.LexicalAspect.achievementProfile
- Semantics.Presupposition.OntologicalPreconditions.cosTypeToAspectualProfile Semantics.Lexical.Verb.ChangeOfState.CoSType.continuation = Semantics.Tense.Aspect.LexicalAspect.activityProfile
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CoS verbs have specific Vendler classifications (derived from profile).
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Cessation is classified as achievement (telic, punctual).
Continuation is classified as activity (atelic, durative).
The Vendler class determines the telicity correctly.
Classification of entailment relations between a sentence and its implied content (@cite{roberts-simons-2024} §2.1).
- precondition : EntailmentRelation
Temporally prior, enables the event. Projects by pragmatic default.
- consequence : EntailmentRelation
Temporally posterior, results from the event. At-issue.
- concomitant : EntailmentRelation
Mereological part or co-occurring state. At-issue. Example: "Jane shouted" entails "Jane made sound" — the sound-making is part of the shouting, not a precondition for it.
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Only precondition entailments project by pragmatic default.
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"Know C" as an event phase: stative, atelic. Precondition: C is true. The knowing state cannot exist without its object. The state persists without change, so consequence = precondition = C.
Equations
- Semantics.Presupposition.OntologicalPreconditions.knowAsEventPhase BEL C = { precondition := C, eventOccurs := fun (w : W) => BEL w && C w, consequence := C }
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"Discover C" as an event phase: telic, achievement. Two preconditions: C is true AND the agent was previously ignorant. The discovery transitions from ignorance to knowledge. Consequence: C is (still) true and the agent is no longer ignorant.
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"Regret p" as an event phase: emotive factive. Precondition: agent believes p (the emotion ontologically depends on the belief, not on truth directly).
@cite{roberts-simons-2024} (p. 731): regret's factivity arises from a pragmatic default to veridicality — in the absence of an explicit claim that the agent is mistaken, emotive attitudes are taken to be veridical. The ontological precondition is belief, not truth.
Equations
- Semantics.Presupposition.OntologicalPreconditions.regretAsEventPhase BEL = { precondition := BEL, eventOccurs := BEL, consequence := BEL }
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Know is atelic: no state change (precondition = consequence).
Both know and discover have C as (part of) their precondition. This is the shared factivity: complement truth is ontologically required.
Discover's precondition additionally requires prior ignorance. This extra precondition (ignorance of C) explains why discover has weaker projection than know in conditional antecedents: in "If I discover p", the speaker's ignorance of p is salient, suppressing projection of C (@cite{roberts-simons-2024} §3.2.2).
Continue has a precondition (prior activity) but involves NO state change.
@cite{roberts-simons-2024} (p. 734): "continue V-ing is atelic, without a
pre-state" in the CoS sense. The CoSType.continuation classification is
a convenience; the key structural fact is isAtelic.
A selectional restriction as an event phase.
The requirement is an ontological precondition of the event.
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- Semantics.Presupposition.OntologicalPreconditions.selectionalEventPhase requirement event = { precondition := requirement, eventOccurs := event, consequence := event }
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Selectional restrictions are well-formed: the event entails the requirement.
Selectional restrictions project through negation (same aboutness mechanism).
Conditions under which projection of a precondition is suppressed. When any of these obtains, the hearer does not accommodate the precondition into the global context.
- preconditionKnownFalse : SuppressionCondition
Interlocutors know or believe the precondition is false or controversial. Example: discussing politics with someone who denies the premise. (@cite{roberts-simons-2024} ex. 23)
- speakerNonCommitment : SuppressionCondition
Evidence that the speaker does not believe the precondition. Example: "I doubt that. Mary would divorce him if she discovered he was drinking." — speaker explicitly doubts the drinking. (@cite{roberts-simons-2024} ex. 24)
- preconditionAtIssue : SuppressionCondition
The precondition is at-issue (currently under discussion). Example: "Is there a decision on Jane's tenure case?" "She isn't aware that there's been a decision." — decision existence is QUD. (@cite{roberts-simons-2024} ex. 25)
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When suppression applies, precondition content is merely locally entailed, not globally accommodated. The content is still an entailment of the trigger — it simply isn't taken to be part of the speaker's presumptions.