Alonso-Ovalle & Royer (2024): modal indefinites and semantic variation in Chuj #
Chuj yalnhej DPs are existential quantifiers with an at-issue modal component (59): some
member of the domain satisfies restrictor and scope, and every member does so in some world of
the content of the DP's event anchor (ModalExists, on Modality.contentPossibility). The DP's
event variable is bound by the abstraction over the VP event (62), left free and read as the
assertion (69)/(71), or bound by an external modal's anchor (87)/(91). A VP event projects the
worlds where the decision that caused it is fulfilled, which gives random choice: an
indiscriminate decision, or one to take everything, satisfies the component and a decision for
one item does not (randomChoice, Fig. 1, (32)–(33)). The assertion projects the speaker's
doxastic alternatives, which gives an epistemic component compatible with any degree of
ignorance and with knowing that the whole domain qualifies, but not with knowing which proper
part does (epistemic, Figs. 2–3, (29)). A non-volitional verb's event has no decision
(nonvolitional, (34)), and an external argument merges above the VP abstraction, so the
flavors available at a site follow from the binders that reach it (flavors_pattern, §3.4,
fn. 17). Under an imperative the anchor can be the order's (harmonic, (82)–(85)).
Modal indefinites vary in the anchors they admit and in the bound on their witnesses (§6.2).
Uno cualquiera admits only anchors with normative conditions, decisions and orders, as
Alonso-Ovalle and Menéndez-Benito argue, so it has no epistemic reading but has the harmonic one
under an imperative (cualquiera_selective, (67)–(68), (86), (93)); n'importe quel (120) and
Italian un N qualsiasi (121) are as selective. Yalnhej's claim has no upper bound, where
algún's excludes the whole domain and uno cualquiera's requires a unique witness
(upperBound_universal, (122)–(127)). The readings the rows list follow from the denotations
(reading_rows).
Implementation notes #
- A world records which of two items the agent took, and a scenario fixes the worlds each event projects. (59)'s condition that the possible event be similar to the actual one (fn. 14) is left out: a possible world in the content of the anchor verifies the scope of a member.
- A component has its anchor's flavor. A decision gives random choice, a circumstantial flavor; the assertion and the order give the primary flavors Hacquard assigns the declarative and imperative speech acts; a belief state gives an epistemic flavor.
- The bounds of algún and uno cualquiera (p. 31), the first a quantity implicature (p. 32), are part of the assertion here.
- The paper reports only unembedded readings of n'importe quel and un N qualsiasi, and §6.2 ascribes such selectivity to the anchors an item admits. The study gives both uno cualquiera's anchors; un N qualsiasi, the "potential Italian counterpart of uno cualquiera" (p. 32), also its unique witness, which Chierchia derives by scalar competition with the numeral.
- The at-issue status of the components (
survivesrows, §§3.3, 6.1), the unremarkable readings and the predicative uses (§5) are row data: the study models neither embedding under negation nor predication.
TODO #
- Under an overt possibility modal un N qualsiasi has an epistemic reading (Chierchia's (31a)), which uno cualquiera's anchors exclude ((93)); the scenario has no overt epistemic modal to state the contrast.
- No source gives n'importe quel an upper bound or denies it one.
- Fn. 18 ties the missing upper bound to yalnhej's number neutrality.
References #
The schema (59) #
The truth condition (59) holds when some member of D satisfies restrictor and scope and
every restrictor member satisfies the scope in some world of the content of the anchoring
event e.
Equations
- AlonsoOvalleRoyer2024.ModalExists con D P Q e w = ((∃ x ∈ D, P x w ∧ Q x w) ∧ ∀ y ∈ D, P y w → Modality.contentPossibility con (Q y) e)
Instances For
A unique member of D satisfies restrictor and scope, the bound of uno cualquiera
(p. 31).
Equations
- AlonsoOvalleRoyer2024.UniqueWitness D P Q w = ∃ x ∈ D, P x w ∧ Q x w ∧ ∀ y ∈ D, P y w → Q y w → y = x
Instances For
Not every restrictor member satisfies the scope, the weaker bound of algún (p. 31).
Equations
- AlonsoOvalleRoyer2024.NotAll D P Q w = ¬∀ x ∈ D, P x w → Q x w
Instances For
Equations
- AlonsoOvalleRoyer2024.instDecidableUniqueWitnessOfDecidableEq D P Q w = id inferInstance
Equations
- AlonsoOvalleRoyer2024.instDecidableNotAll D P Q w = id inferInstance
Events and what they project #
There are two items, and a world records which of them the agent took (bought, liked, grabbed).
Equations
- AlonsoOvalleRoyer2024.Item = Fin 2
Instances For
Equations
Instances For
Equations
- AlonsoOvalleRoyer2024.instDecidableEqEv x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
A scenario fixes the worlds each event projects, namely those where the decision that caused the VP event is fulfilled, if the verb is volitional, the speaker's doxastic alternatives, the addressee's to-do list and the attitude holder's belief state.
Instances For
scenario builds a scenario from the decision and the doxastic alternatives, with an
optional order and belief state.
Equations
- AlonsoOvalleRoyer2024.scenario decision dox todo belief = { decision := decision, dox := dox, todo := todo, belief := belief }
Instances For
s.worlds e is the set of worlds the event e projects in s, if any.
Equations
- s.worlds AlonsoOvalleRoyer2024.Ev.vp = s.decision
- s.worlds AlonsoOvalleRoyer2024.Ev.assertion = some s.dox
- s.worlds AlonsoOvalleRoyer2024.Ev.order = some s.todo
- s.worlds AlonsoOvalleRoyer2024.Ev.belief = some s.belief
Instances For
Equations
- AlonsoOvalleRoyer2024.instDecidableContentPossibilityEvWorldContentOfDecidablePred s q e = decidable_of_iff (∃ d ∈ s.worlds e, ∃ w ∈ d, q w) ⋯
An event projects a component of its own flavor. The decision behind a VP event gives random choice, a circumstantial flavor, the assertion and the order the primary flavors of the declarative and imperative speech acts, and a belief state an epistemic flavor.
Equations
- AlonsoOvalleRoyer2024.Ev.vp.flavor = Modality.ModalFlavor.circumstantial
- AlonsoOvalleRoyer2024.Ev.assertion.flavor = Discourse.SpeechAct.Force.declarative.primaryFlavor
- AlonsoOvalleRoyer2024.Ev.order.flavor = Discourse.SpeechAct.Force.imperative.primaryFlavor
- AlonsoOvalleRoyer2024.Ev.belief.flavor = Modality.ModalFlavor.epistemic
Instances For
Equations
- AlonsoOvalleRoyer2024.instDecidableClaim s e w = id (id inferInstance)
nonempty is the set of worlds in which something was taken.
Equations
- AlonsoOvalleRoyer2024.nonempty = Finset.filter Finset.Nonempty Finset.univ
Instances For
In Fig. 1 and (32)–(33), the indiscriminate decision buy a book and the decision buy all books satisfy the modal component, and the decision buy b₁ does not.
In Figs. 2–3 and (29), the component anchored to the assertion holds under total or partial ignorance and when the speaker knows the whole domain qualifies, but not when the speaker knows which proper part does.
Under the imperative of (82)–(85), projection from the addressee's deliberate decision fails, while projection from the order, which permits any card, succeeds.
Position and flavor (§3.4) #
Equations
- AlonsoOvalleRoyer2024.instDecidableEqSite x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
Instances For
At a site, the DP's event variable can be bound to the VP event where its abstraction c-commands the DP, to an external modal's anchor when embedded under one, and to the assertion when left free (fn. 17).
Equations
- AlonsoOvalleRoyer2024.binders site embedded = (if site.belowVPAbstraction = true then [AlonsoOvalleRoyer2024.Ev.vp] else []) ++ embedded.toList ++ [AlonsoOvalleRoyer2024.Ev.assertion]
Instances For
A DP at a site can express the flavors of those of its binders that project worlds in the scenario.
Equations
- One or more equations did not get rendered due to their size.
Instances For
An external argument is epistemic only, and an internal argument or adjunct is random choice or epistemic with a volitional verb and epistemic only with a non-volitional one (§3.4).
Items (§§4, 6.2) #
The item's denotation anchored to e is defined when the item admits the anchor and true
when the claim holds within the bound.
Equations
- i.denotation s e w = if i.Admits s e then SignType.ofProp (AlonsoOvalleRoyer2024.Claim s e w ∧ i.Bound w) else 0
Instances For
The decision behind a volitional event and an order have normative conditions; a speech event and a belief state do not, having informational content (p. 35, after [AOMB18] pp. 29, 31).
Equations
- s.Normative AlonsoOvalleRoyer2024.Ev.vp = (s.decision.isSome = true)
- s.Normative AlonsoOvalleRoyer2024.Ev.order = True
- s.Normative AlonsoOvalleRoyer2024.Ev.assertion = False
- s.Normative AlonsoOvalleRoyer2024.Ev.belief = False
Instances For
Equations
- AlonsoOvalleRoyer2024.instDecidablePredEvNormative s AlonsoOvalleRoyer2024.Ev.vp = AlonsoOvalleRoyer2024.instDecidablePredEvNormative._aux_1 s
- AlonsoOvalleRoyer2024.instDecidablePredEvNormative s AlonsoOvalleRoyer2024.Ev.order = instDecidableTrue
- AlonsoOvalleRoyer2024.instDecidablePredEvNormative s AlonsoOvalleRoyer2024.Ev.assertion = instDecidableFalse
- AlonsoOvalleRoyer2024.instDecidablePredEvNormative s AlonsoOvalleRoyer2024.Ev.belief = instDecidableFalse
Yalnhej admits any anchor and has no bound (§4.2).
Equations
- One or more equations did not get rendered due to their size.
Instances For
Uno cualquiera admits normative anchors and requires a unique witness (p. 31).
Equations
- One or more equations did not get rendered due to their size.
Instances For
N'importe quel admits normative anchors (120).
Equations
- One or more equations did not get rendered due to their size.
Instances For
Uno cualquiera is undefined anchored to the assertion or a belief state, so it has no epistemic reading ((67)–(68), (93)), but anchored to the order of (86) it is defined, and an order that any card fulfils verifies it.
N'importe quel conveys random choice and is undefined anchored to the assertion (120).
Where everything was taken, because everyone danced (124)–(125) or Xun bought all the books (126)–(127), yalnhej's claim holds, while algún's bound (122) and uno cualquiera's unique witness (123) fail.
The paper's judgments #
readingFlavor gives the flavor of the reading a row names.
Equations
- AlonsoOvalleRoyer2024.readingFlavor "epistemic" = some Modality.ModalFlavor.epistemic
- AlonsoOvalleRoyer2024.readingFlavor "random choice" = some Modality.ModalFlavor.circumstantial
- AlonsoOvalleRoyer2024.readingFlavor x✝ = none
Instances For
doxOf gives the doxastic alternatives a row's epistemicState names, with {0} the
actual world.
Equations
- AlonsoOvalleRoyer2024.doxOf "ignorant" = some AlonsoOvalleRoyer2024.nonempty
- AlonsoOvalleRoyer2024.doxOf "knows which, not all" = some {{0}}
- AlonsoOvalleRoyer2024.doxOf "knows all" = some {{0, 1}}
- AlonsoOvalleRoyer2024.doxOf x✝ = none
Instances For
decisionOf gives the decision a row's decision feature names.
Equations
- AlonsoOvalleRoyer2024.decisionOf "indiscriminate" = some AlonsoOvalleRoyer2024.nonempty
- AlonsoOvalleRoyer2024.decisionOf "specific" = some {{0}}
- AlonsoOvalleRoyer2024.decisionOf "all" = some {{0, 1}}
- AlonsoOvalleRoyer2024.decisionOf x✝ = none
Instances For
A position row is predicted acceptable iff some binder available at its site projects the reading's flavor and, when the row gives a scenario, the claim anchored there holds.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Every Chuj position row carries the predicted judgment.
itemOf gives the item a row's item feature names, among those the study gives a
denotation. Un N qualsiasi is uno cualquiera's Italian counterpart (p. 32); algún and
irgendein, whose modal components are implicatures (§6.1), and the modifier komon have
none here.
Equations
- AlonsoOvalleRoyer2024.itemOf "yalnhej" = some AlonsoOvalleRoyer2024.yalnhej
- AlonsoOvalleRoyer2024.itemOf "uno cualquiera" = some AlonsoOvalleRoyer2024.cualquiera
- AlonsoOvalleRoyer2024.itemOf "un qualsiasi" = some AlonsoOvalleRoyer2024.cualquiera
- AlonsoOvalleRoyer2024.itemOf "n'importe quel" = some AlonsoOvalleRoyer2024.nimporteQuel
- AlonsoOvalleRoyer2024.itemOf x✝ = none
Instances For
A reading of flavor fl is available unembedded when a binder of an object (62), (69) of
that flavor makes the item defined and true given an indiscriminate decision and an ignorant
speaker.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Equations
- AlonsoOvalleRoyer2024.instDecidableAvailable i fl = id inferInstance
A row is bare when it embeds the item nowhere and fixes no position, anchor, scenario or continuation.
Equations
- AlonsoOvalleRoyer2024.IsBare row = ∀ f ∈ ["position", "survives", "embedded", "anchor", "scenario", "continuation", "construction", "property"], row.feature? f = none
Instances For
Equations
- AlonsoOvalleRoyer2024.instDecidableIsBare row = id inferInstance
In every bare row of an item the study analyses, the judgment of the reading the row names and of each reading it lists is acceptable iff the item makes it available ((54), (93), (119)–(121), fn. 20 (i)).