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Studies.AlonsoOvalleRoyer2024

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 #

TODO #

References #

The schema (59) #

def AlonsoOvalleRoyer2024.ModalExists {E : Type u_1} {W : Type u_2} {X : Type u_3} (con : E → Option (Set W)) (D : Finset X) (P Q : X → W → Prop) (e : E) (w : W) :

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.

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    def AlonsoOvalleRoyer2024.UniqueWitness {W : Type u_2} {X : Type u_3} (D : Finset X) (P Q : X → W → Prop) (w : W) :

    A unique member of D satisfies restrictor and scope, the bound of uno cualquiera (p. 31).

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      def AlonsoOvalleRoyer2024.NotAll {W : Type u_2} {X : Type u_3} (D : Finset X) (P Q : X → W → Prop) (w : W) :

      Not every restrictor member satisfies the scope, the weaker bound of algún (p. 31).

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        instance AlonsoOvalleRoyer2024.instDecidableUniqueWitnessOfDecidableEq {W : Type u_2} {X : Type u_3} (D : Finset X) (P Q : X → W → Prop) (w : W) [(x : X) → Decidable (P x w)] [(x : X) → Decidable (Q x w)] [DecidableEq X] :
        Decidable (UniqueWitness D P Q w)
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        instance AlonsoOvalleRoyer2024.instDecidableNotAll {W : Type u_2} {X : Type u_3} (D : Finset X) (P Q : X → W → Prop) (w : W) [(x : X) → Decidable (P x w)] [(x : X) → Decidable (Q x w)] :
        Decidable (NotAll D P Q w)
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        Events and what they project #

        @[reducible, inline]

        There are two items, and a world records which of them the agent took (bought, liked, grabbed).

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            Item y is among what was taken.

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              A scenario has four events, the VP event, the assertion, an order and a belief.

              • vp : Ev
              • assertion : Ev
              • order : Ev
              • belief : Ev
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                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.

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                  def AlonsoOvalleRoyer2024.scenario (decision : Option (Finset World)) (dox todo belief : Finset World := ∅) :

                  scenario builds a scenario from the decision and the doxastic alternatives, with an optional order and belief state.

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                    s.worlds e is the set of worlds the event e projects in s, if any.

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                      The content of an event is (59)'s domain-fixing function.

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                        theorem AlonsoOvalleRoyer2024.contentPossibility_content (s : Scenario) (q : World → Prop) (e : Ev) :
                        Modality.contentPossibility s.content q e ↔ ∃ d ∈ s.worlds e, ∃ w ∈ d, q w
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                        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.

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                          Claim s e is the claim of a yalnhej DP over the whole domain, anchored to e.

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                            @[instance_reducible]
                            instance AlonsoOvalleRoyer2024.instDecidableClaim (s : Scenario) (e : Ev) (w : World) :
                            Decidable (Claim s e w)
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                            nonempty is the set of worlds in which something was taken.

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                              theorem AlonsoOvalleRoyer2024.randomChoice :
                              Claim (scenario (some nonempty)) Ev.vp {0} ∧ Claim (scenario (some {{0, 1}})) Ev.vp {0, 1} ∧ ¬Claim (scenario (some {{0}})) Ev.vp {0}

                              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.

                              theorem AlonsoOvalleRoyer2024.epistemic :
                              Claim (scenario none nonempty) Ev.assertion {0} ∧ Claim (scenario none {{0}, {0, 1}}) Ev.assertion {0} ∧ Claim (scenario none {{0, 1}}) Ev.assertion {0, 1} ∧ ¬Claim (scenario none {{0}}) Ev.assertion {0}

                              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.

                              theorem AlonsoOvalleRoyer2024.nonvolitional (dox todo belief : Finset World) (w : World) :
                              ¬Claim (scenario none dox todo belief) Ev.vp w

                              A non-volitional VP event contains no decision, so nothing projects from it and the random choice reading of (34) is unavailable whatever the world.

                              theorem AlonsoOvalleRoyer2024.harmonic :
                              ¬Claim (scenario (some {{0}}) ∅ {{0}, {1}}) Ev.vp {0} ∧ Claim (scenario (some {{0}}) ∅ {{0}, {1}}) Ev.order {0}

                              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) #

                              A site is the base position of the DP relative to the abstraction over the VP event. An external argument merges above it (74), internal arguments and adjuncts below (62).

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                                def AlonsoOvalleRoyer2024.binders (site : Site) (embedded : Option Ev) :
                                List Ev

                                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).

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                                  def AlonsoOvalleRoyer2024.flavors (s : Scenario) (site : Site) (embedded : Option Ev) :

                                  A DP at a site can express the flavors of those of its binders that project worlds in the scenario.

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                                    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) #

                                    A modal indefinite of the schema (59) varies, as §6.2 describes, in the anchors it admits, a definedness condition, and in the bound on its witnesses.

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                                      The item's denotation anchored to e is defined when the item admits the anchor and true when the claim holds within the bound.

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                                        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).

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                                          Yalnhej admits any anchor and has no bound (§4.2).

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                                            Uno cualquiera admits normative anchors and requires a unique witness (p. 31).

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                                              N'importe quel admits normative anchors (120).

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                                                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).

                                                theorem AlonsoOvalleRoyer2024.upperBound_universal :
                                                yalnhej.denotation (scenario none {{0, 1}}) Ev.assertion {0, 1} = 1 ∧ yalnhej.denotation (scenario (some {{0, 1}})) Ev.vp {0, 1} = 1 ∧ ¬NotAll Finset.univ (fun (x : Item) (x_1 : World) => True) Taken {0, 1} ∧ cualquiera.denotation (scenario (some {{0, 1}})) Ev.vp {0, 1} = -1

                                                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 #

                                                def AlonsoOvalleRoyer2024.doxOf :
                                                String → Option (Finset World)

                                                doxOf gives the doxastic alternatives a row's epistemicState names, with {0} the actual world.

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                                                  def AlonsoOvalleRoyer2024.decisionOf :
                                                  String → Option (Finset World)

                                                  decisionOf gives the decision a row's decision feature names.

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                                                    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.

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                                                      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.

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                                                        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.

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                                                          A row is bare when it embeds the item nowhere and fixes no position, anchor, scenario or continuation.

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                                                            instance AlonsoOvalleRoyer2024.instDecidableIsBare (row : Datum) :
                                                            Decidable (IsBare row)
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                                                            theorem AlonsoOvalleRoyer2024.reading_rows (row : Datum) :
                                                            row ∈ Examples.all → IsBare row → ∀ i ∈ (row.feature? "item").bind itemOf, (∀ fl ∈ (row.feature? "reading").bind readingFlavor, (row.judgment == Judgment.acceptable) = decide (i.Available fl)) ∧ ∀ r ∈ row.readings, ∀ fl ∈ readingFlavor r.1, (r.2 == Judgment.acceptable) = decide (i.Available fl)

                                                            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)).