Event Projection → Temporal Orientation #
[Hac06] [Hac10] [Con02] [Kra12]Derives the temporal orientation of modals from event projection. High modals get the speech time (present perspective); low modals get the event time (past perspective).
The Pattern #
| Position | Event binder | holder(e) | τ(e) | Temporal orientation |
|---|---|---|---|---|
| High (above Asp) | speech act e₀ | speaker | speech time (now) | Present |
| Low (below Asp) | VP event e₂ | agent | event time (then) | Past/event-local |
Hacquard's Derivation #
Individual-time pairs are DERIVED from events via projection functions
holder(e) and τ(e). Since high modals bind to the speech event and
low modals bind to the VP event, their temporal parameters differ:
- "Jane a dû prendre le train" ([Hac06], (201)):
- Epistemic (high): τ(e₀) = now → "Given my evidence NOW,..."
- Root (low): τ(e₂) = then → "Given Jane's circumstances THEN,..."
This connects EventProjection (EventRelativity §11) to the temporal
modal evaluation framework in Temporal.lean.
[Hac06] derives present vs. past from modal position
(§ 3). [Kle16] adds future: derived not from position but
from the modal base kind (CIR permits future orientation). The
canonical 3-value TemporalOrientation lives in
Semantics/Modality/TemporalAxes.lean and is opened above.
A time type for the orientation examples.
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- Hacquard2006.instDecidableEqOTime x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Hacquard2006.instReprOTime = { reprPrec := Hacquard2006.instReprOTime.repr }
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- Hacquard2006.instReprOTime.repr Hacquard2006.OTime.now prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Hacquard2006.OTime.now")).group prec✝
- Hacquard2006.instReprOTime.repr Hacquard2006.OTime.then_ prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Hacquard2006.OTime.then_")).group prec✝
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Two events: speech act and VP event.
- speech : OrientationEvent
The speech event (e₀)
- vpEvent : OrientationEvent
The VP event (e₂)
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- Hacquard2006.instDecidableEqOrientationEvent x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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Individuals: speaker and the described event's agent.
- speaker : OrientationPerson
- agent : OrientationPerson
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- Hacquard2006.instDecidableEqOrientationPerson x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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Event projection for the temporal orientation scenario. Speech events project to (speaker, now); VP events project to (agent, then).
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Speech event projects to speech time (now).
VP event projects to event time (then).
Derive temporal orientation from modal position, via event binding.
High modals (above Asp) bind to the speech event → τ(e₀) = now → present. Low modals (below Asp) bind to the VP event → τ(e₂) = then → past.
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High modals have present temporal orientation.
Low modals have past temporal orientation.
The same modal (devoir, pouvoir) has different temporal perspectives depending on its structural position — derived from event projection, not stipulated.
The temporal orientation derived from event projection connects to
Temporal.lean's time-indexed conversational backgrounds.
When the modal binds to event e with τ(e) = t, the conversational
background is evaluated at time t: f(w,t). The time IS the event's
temporal trace. Event projection subsumes time-indexing: rather than
stipulating which time to evaluate at, the time is projected from
whichever event binds the modal.
([Hac06], (201)): two readings of the same sentence with different temporal perspectives, derived from event binding.
Epistemic (high): "Given MY evidence NOW, Jane must have taken the train." → modal bound to speech event → τ(e₀) = speech time = now → background evaluated at speech time
Root (low): "Given JANE'S circumstances THEN, Jane had to take the train." → modal bound to VP event → τ(e₂) = event time = then → background evaluated at event time
The full derivation chain for "Jane a dû prendre le train": event binding → event projection → temporal orientation.
This is the payoff of event-relative modality: the same modal gets different temporal perspectives from different event bindings, without any stipulation about temporal orientation.
[Hac06] and [Kle16] explain different aspects of temporal orientation:
Hacquard: Position (high/low) determines whether the conversational background is evaluated at speech time (present) or event time (past). This explains the epistemic/root contrast.
Klecha: Modal base kind (DOX/CIR) determines whether future-oriented readings are available. DOX (doxastic) constrains RT ≤ EvalT (upper limit); CIR (circumstantial) permits RT > EvalT (future orientation).
The two theories are complementary: Hacquard tells you WHAT time the modal base is evaluated at; Klecha tells you WHICH DIRECTION of temporal reference is available from that time.
Hacquard's derivation covers present and past orientation. Future orientation is NOT derived from position — it requires [Kle16]'s modal base analysis.
Hacquard's positional analysis does not derive future orientation. Future orientation is orthogonal to position — it is determined by the modal base kind (CIR), not by where the modal is merged.
Bridge: Hacquard ↔ [Con02] #
[Hac06] determines which time the modal base is evaluated at (via event projection); [Con02] determines what modal base types are available at that time (via settledness and diversity).
The half proved here is Hacquard's: position fixes the temporal
perspective and the modal/aspect scope (position_determines_modal_base_type).
On Condoravdi's account this feeds the second half — present perspective +
MODAL > PERF yields a settled, non-diverse past property (epistemic only);
past perspective + PERF > MODAL yields an unsettled future property
(metaphysical available). That machinery lives in
Semantics/Modality/HistoricalAlternatives.lean; chaining the two halves
into one composition theorem is left as follow-up.
Map Hacquard's temporal orientation to Condoravdi's temporal perspective. Future orientation (Klecha 2016) has no Condoravdi analogue — it is orthogonal to the scope–modality correlation.
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- Hacquard2006.toPerspective Semantics.Modality.TemporalOrientation.present = some Semantics.Modality.TemporalPerspective.present
- Hacquard2006.toPerspective Semantics.Modality.TemporalOrientation.past = some Semantics.Modality.TemporalPerspective.past
- Hacquard2006.toPerspective Semantics.Modality.TemporalOrientation.future = none
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High modals (above Asp) have Condoravdi's present perspective.
Low modals (below Asp) have Condoravdi's past perspective.
The key derivation chain: position determines both perspective AND aspect scope, and these two together determine which modal base types are available.
High (above Asp): present perspective + modal over aspect. MODAL > PERF scoping → the property under the modal is past → settled → diversity fails → metaphysical blocked → epistemic only.
Low (below Asp): past perspective + aspect over modal. PERF > MODAL scoping → the property under the modal is future (of the past event time) → not settled → diversity satisfiable → metaphysical available.
This connects Hacquard's structural account to Condoravdi's temporal one without either stipulating anything.
Bridge content (merged from ActualityInferencesBridge.lean) #
Actuality Inference Data (Cross-Linguistic) #
Cross-linguistic empirical data on actuality inferences with ability modals.
Key Generalization ([Nad23a], Chapter 1) #
Across languages, ability modals with perfective aspect entail the complement, while those with imperfective aspect do not.
| Language | Modal | PFV entails? | IMPF entails? |
|---|---|---|---|
| Greek | boro | Yes | No |
| Hindi | saknaa | Yes | No |
| French | pouvoir | Yes | No |
| English | be able | Yes (episodic) | No (habitual) |
A single cross-linguistic data point for actuality inferences.
- language : String
Language name
- modalForm : String
The modal form in that language
- aspect : Semantics.Aspect.ViewpointAspectB
Viewpoint aspect of the sentence
- complementEntailed : Bool
Does the complement entailment hold?
- gloss : String
Example sentence gloss
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Greek boro + perfective (aorist): "She was-able.PFV to swim across" → She swam across.
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Greek boro + imperfective: "She was-able.IMPF to swim across" ↛ She swam across.
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Hindi saknaa + perfective: "She was-able.PFV to swim across" → She swam across.
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Hindi saknaa + imperfective: "She was-able.IMPF to swim across" ↛ She swam across.
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French pouvoir + passé composé (perfective): "She was-able.PFV to swim across" → She swam across.
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French pouvoir + imparfait (imperfective): "She was-able.IMPF to swim across" ↛ She swam across.
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English be able + episodic (perfective-like): "She was able to swim across" → She swam across.
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English be able + habitual (imperfective-like): "She was able to swim across" ↛ She swam across on that occasion.
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All actuality inference data points.
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The perfective subset.
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The imperfective subset.
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All 4 perfective data points have complementEntailed = true.
All 4 imperfective data points have complementEntailed = false.
Central empirical generalization: across all 8 data points,
complementEntailed tracks aspect ==.perfective exactly.
This is the empirical observation that [Nad23a] explains via the causal sufficiency + aspect interaction.
We have data from 4 distinct languages.
Each language contributes exactly one perfective and one imperfective datum.
Every datum's complementEntailed field matches the position × aspect
prediction for root modals. All data involves root/ability modals
(below AspP), so the prediction is actualityEntailmentPredicted.belowAsp d.aspect.
This connects the theory-neutral empirical data (§§ above) to [Hac06]'s structural explanation: root modals are below Asp, so perfective forces actualization.
Per-language bridge: Greek data matches position theory.
Per-language bridge: Hindi data matches position theory.
Per-language bridge: French data matches position theory.
Per-language bridge: English data matches position theory.