Actuality Entailments: Position × Aspect #
@cite{hacquard-2006} @cite{hacquard-2009} @cite{bhatt-1999}
Derives actuality entailments from the relative scope of aspect and
modal, building on event-relative modality (EventRelativity.lean).
The Puzzle #
The same modal verb shows different entailment patterns depending on interpretation (@cite{bhatt-1999}, @cite{hacquard-2006} Ch.1):
- Root (ability) + PFV: "Jane a pu prendre le train" → she took it
- Root (ability) + IMPF: "Jane pouvait prendre le train" → maybe not
- Epistemic + PFV: "Jane a pu prendre le train" → maybe not
@cite{hacquard-2006}'s Solution #
The relative position of the modal determines which event binder captures it:
Root modals (below AspP):
[AspP PRFV [ModP can [VP take train]]]Perfective quantifies over the entire modal+VP event → actualization.Epistemic modals (above AspP):
[ModP can [AspP PRFV [VP take train]]]Modal scopes over perfective → perfective applies to VP only in accessible worlds → no actualization in the actual world.
Content Licensing Explains the Asymmetry #
WHY are epistemic modals always above aspect? Content licensing (EventRelativity §8): epistemic modal bases require a contentful event. VP events lack content. Therefore epistemic modals cannot be bound by aspect — they must be above AspP. Root modals need only circumstantial backgrounds (any event type), so they CAN be below AspP.
The actuality entailment asymmetry follows from content licensing + aspect scope, without stipulation.
The earlier CausalFrame-bridge §4 (showing actualityWithAspect .perfective
matches sufficientAt ∧ actualizedAt) was deleted in Phase D-H along with
the CausalFrame/ComplementEntailing substrate; the qualitative bridge to
@cite{nadathur-2023}'s causal account now lives at the V2 SEM level in
study files and Semantics/Causation/.
The relative scope of aspect and the modal in the clause structure.
Root modals are below AspP: aspect quantifies over the modal event. Epistemic modals are above AspP: the modal quantifies over aspect.
This structural difference — not lexical semantics — is the sole source of the actuality entailment asymmetry.
- aspectOverModal : AspectModalScope
Root: [Asp [Mod [VP]]] — aspect scopes over modal
- modalOverAspect : AspectModalScope
Epistemic: [Mod [Asp [VP]]] — modal scopes over aspect
Instances For
Equations
- Semantics.Modality.ActualityEntailments.instDecidableEqAspectModalScope x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- One or more equations did not get rendered due to their size.
Instances For
Position determines aspect scope. belowAsp → aspect over modal (root configuration). aboveAsp → modal over aspect (epistemic configuration).
Equations
- Semantics.Modality.ActualityEntailments.toAspectScope Semantics.Modality.EventRelativity.ModalPosition.belowAsp = Semantics.Modality.ActualityEntailments.AspectModalScope.aspectOverModal
- Semantics.Modality.ActualityEntailments.toAspectScope Semantics.Modality.EventRelativity.ModalPosition.aboveAsp = Semantics.Modality.ActualityEntailments.AspectModalScope.modalOverAspect
Instances For
Whether the theory predicts an actuality entailment for a given position × aspect combination.
Only root + perfective yields an actuality entailment:
| Position | Aspect | AE? | Why |
|---|---|---|---|
| root (below Asp) | PFV | ✓ | Asp > Mod: PFV forces completion |
| root (below Asp) | IMPF | ✗ | Asp > Mod: IMPF doesn't force completion |
| epistemic (above Asp) | PFV | ✗ | Mod > Asp: PFV in accessible worlds only |
| epistemic (above Asp) | IMPF | ✗ | Mod > Asp: no completion |
Equations
Instances For
Only root + perfective yields actuality entailments. This is a characterization result: AE ↔ (belowAsp ∧ perfective).
The prediction aligns with the aspect scope story: AE holds exactly when aspect scopes over the modal AND aspect is perfective.
The same lexical modal yields different actuality patterns depending solely on position. This is Hacquard's core argument against lexical ambiguity: French pouvoir, Greek boro, Hindi saknaa are single lexical items whose actuality behavior is structurally determined.
WHY are epistemic modals always above aspect? Content licensing (EventRelativity §8) provides the answer:
- Epistemic modal bases require CON(e) — propositional content.
- VP events (running, swimming) lack propositional content.
- Aspect binds modals to VP events.
- Therefore: a modal bound by aspect CANNOT be epistemic.
- Therefore: epistemic modals are necessarily above AspP.
- Therefore: perfective never scopes over epistemic modals.
- Therefore: no actuality entailment for epistemics.
The chain: content licensing → position → scope → (no) AE.
The full explanatory chain from content licensing to actuality entailments, linking EventRelativity §§8–9 to @cite{hacquard-2006} Ch.1.
Epistemic modals are necessarily high (above Asp), because low modals are bound to VP events which lack content.
The actuality entailment pattern results from the interaction of content licensing, syntactic position, and viewpoint aspect.
This theorem chains together:
- EventRelativity §8 (content licensing determines available flavors)
- EventRelativity §9 (position determines event binder)
- This file §1–2 (position determines aspect scope → AE prediction)
The causal-model validation of the root + PFV case (formerly via
CausalFrame/ComplementEntailing) is now witnessed at the V2 SEM level
in study files.