Hacquard (2006): Aspects of Modality #
This file formalizes [Hac06]'s derivation of actuality entailments and its
event-relative semantics for modal auxiliaries. Perfective aspect is a quantifier over events
anchored to a world (72a), perfective; when tense sits above a root modal, aspect moves above
the modal, so its event is bound in the actual world while the modal binds only the world in
which the event is described (75). With the principle of Event Identification across Worlds
(76), IdentifiesAcrossWorlds, the actual event is then a Q-event in the actual world:
actuality_of_rootPossibility and actuality_of_rootNecessity are [Bha99]'s actuality
entailment for the possibility and necessity modals (86), (87), and the goal that restricts a
goal-oriented modal need not hold in the actual world (88). A modal above aspect binds the
world in which the event occurs, so no actuality follows, epistemicPossibility_not_actual;
and the imperfective's GEN (130) binds the event variable itself and needs no verifying
instance, gen_not_actual, which is why root modals under imperfective are not implicative
(100). Chapter 3 relativizes the accessibility relation to an event bound by the closest
binder, aspect, the speech event, or an attitude (200), (309), so a modal is keyed to that
event's participants and time (201), positionPerspective; an epistemic relation needs an
event with content (310a), so an aspect-bound modal is epistemic only under a contentful
complement, not_aspectBoundEpistemic_of_eq_none, and its reading (248) is an epistemic
necessity for the attitude holder, aspectBoundEpistemic_iff. The starting point of the
account is that one modal verb has root and epistemic readings alike, as Italian potere and
dovere do, italian_modals_one_entry, so the contrast in actuality entailments cannot be
lexical. The dissertation's examples are the rows of Data.Examples.Hacquard2006.
Implementation notes #
Events, worlds, and times are arbitrary types with an occurrence relation and a running time;
event descriptions are predicates of an event and a world, and a description is assumed to hold
of an event only where it occurs. Modal bases are functions from events to sets of worlds, the
content of an event is partial, and the epistemic readings are
Semantics/Modality/EventRelativity.lean's quantifiers over it. The binding conditions (200)
and (309) are syntactic and enter only through which event a modal is anchored to; the
progressive (124) and the counterfactual modal of chapter 2, Italian volere (chapter 4), and
the interaction with negation (84) are not formalized.
References #
One entry per modal, chapter 1 #
Each Italian modal verb keeps one force across an epistemic and a root flavor, the pattern that argues for a single entry whose reading is fixed by structure.
Aspect as a world-anchored quantifier over events, chapter 1 #
Perfective aspect (72a) holds when an event of the world whose running time lies within the reference time satisfies the predicate.
Equations
- Hacquard2006.perfective occurs τ w t P = ∃ (e : E), occurs e w ∧ τ e ⊆ t ∧ P e
Instances For
A root modal below aspect (75) takes the event aspect quantifies over as its event variable and binds the world in which that event is described.
Equations
- Hacquard2006.rootPossibility f Q e = ∃ w' ∈ f e, Q e w'
Instances For
The necessity modal below aspect (87).
Equations
- Hacquard2006.rootNecessity f Q e = ∀ w' ∈ f e, Q e w'
Instances For
Event Identification across Worlds (76) says that an event that occurs in two worlds and is
a Q-event in one is a Q-event in the other.
Equations
- Hacquard2006.IdentifiesAcrossWorlds occurs Q = ∀ (e : E) (w₁ w₂ : W), occurs e w₁ → occurs e w₂ → Q e w₁ → Q e w₂
Instances For
A description holds of an event only in worlds where the event occurs.
Equations
- Hacquard2006.DescribesOccurrence occurs Q = ∀ (e : E) (w : W), Q e w → occurs e w
Instances For
A root possibility modal under perfective aspect entails that the actual event is a
Q-event in the actual world, the unmodalized perfective sentence (75), (86), (89a).
The necessity modal (87) has the same entailment, given an accessible world.
Necessity entails possibility (89), so with the entailment in place the two differ in whether the accessible worlds leave Jane other options; the desirability inference of (89b) is the scalar implicature from not asserting (89c).
A modal above aspect (chapter 3) binds the world of aspect's restriction, so the event occurs in an accessible world.
Equations
- Hacquard2006.epistemicPossibility occurs τ acc t Q = ∃ w' ∈ acc, Hacquard2006.perfective occurs τ w' t fun (x : E) => Q x w'
Instances For
There is no actuality entailment above aspect. An event of an accessible world need not occur in the actual one, so the epistemic reading of (1b) holds while the perfective sentence fails.
The imperfective, chapter 2 #
GEN (130) is the generic operator under a selection function of the normal or ideal events
from the perspective of w at t: it holds when every ideal event meeting the contextual
restriction satisfies the predicate. It binds the event variable itself, so it requires no
verifying instance.
Equations
- Hacquard2006.gen ideal restr w t P = ((w, t) ∈ (Genericity.Normality.ofAccess fun (i : W × Set T) => ideal i.1 i.2).gen {e : E | restr e} {e : E | P e})
Instances For
A root modal under GEN is not implicative (93), (100). Where nothing counts as an
ideal event the generic holds, and no event of the actual world need be a Q-event.
Event-relative modality, chapters 3 and 4 #
Perspective of the anchoring event in a past-tense clause (200), (309): the speech event sits at the utterance time, an attitude or the event quantified by aspect at the time tense provides.
Equations
Instances For
The perspective a modal's position determines in a matrix clause (201), through the event its closest binder supplies.
Equations
Instances For
The same modal gets different temporal perspectives from different positions (201).
Embedded under a past attitude, a high modal is keyed to the attitude time, so the perspective tracks the binder and not the position.
The aspect-bound epistemic reading of a modal over an attitude complement (248c), (248d).
There was an attitude state of the subject within the reference time, and some world
compatible with its content is such that all worlds compatible with it are Q-worlds.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The reading (248) is an epistemic necessity for the attitude holder, a past belief state
with consistent content that entails Q.
The reading exists only because the thinking event has content (310a). Where the events of the actual world have none, as with the train-taking of (246), an aspect-bound modal has no epistemic reading.