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Studies.Tay2024

Tay (2024): Resultative Expressions in Mandarin Chinese #

This file formalizes Tay's account of why Mandarin V-V resultatives realize their arguments more freely than V-de resultatives and English resultatives. A V-V resultative is a synthetic compound built in morphology, V1-∅-V2, so its components are inaccessible to syntactic operations, chapter 2: a locative can modify V1 of a V-de resultative but not of the compound, (45)–(46), and repeatedly has only the whole-event reading on the compound, (41)–(44). The null affix ∅ introduces a macroevent containing a causing event described by V1 and a caused event described by V2, inherits every argument of V2, and existentially closes every argument of V1 (110), nullAffix; the variant ∅+C also names the crucial contributory factor of the macroevent (111), nullAffixC. The factor is a function of the macroevent, so a change has one, ccf_unique, and V1's arguments are closed, so nothing relates the arguments of the compound to those of V1, nullAffix_of: the external argument can be V1's agent (131)–(132) or its theme (133)–(134), the internal argument need not be V1's agent (202)–(206), and the sole argument of an unaccusative compound can be V1's agent (219), which is why Mandarin has subject-oriented resultatives without a reflexive.

What does constrain the external argument is the Onset Condition of [Kim24], (141): an event integrated into the macroevent of a simplex causative is the initial event of its causal chain, Model.Onset. The factor is a participant in that initial event, Model.CcfInitial, and V1's event is integrated, so the factor is a participant in V1's event, participant_of_nullAffixC: no pure causers (146)–(149), while subject matters are participants (150)–(151). On the causal chain of chén 'sink' (136), jī-chén 'strike-sink' names the onset and *chōng-chén 'rush-sink' an event downstream of it, (137)–(140), onsetCondition_strike and not_onsetCondition_rush: on a model of (136) the first meets the Onset Condition and puts the Russian forces in V1's event, ji_chen_participant, and the second violates it, not_sinkingModel_rush_onset. The rows carry the paper's reading of the external argument, and a transitive compound is ungrammatical exactly where that reading is a pure causer, ungrammatical_iff_pureCauser. The macroevent must contain the two subevents rather than identify or nest them: in shè-sǐ 'shoot dead' (107) the shooting and the dying overlap at the moment of contact only, so their traces are neither equal nor nested, shooting_trieventive. Chapter 8's typology varies whether the null head merges in morphology, whether the result X can be a verb, and whether a transitive resultative takes an intransitive X; the third follows from whether the language's change-of-state verbs alternate, since an intransitive one that does not carries no factor and the null head supplies it, ResultativeType.intransitiveX, with Mandarin's pò (684)–(686) the witness, po_not_alternating.

Implementation notes #

Predicates take their arguments as tuples Fin n → D, so a family of null affixes indexed by the arities of V1 and V2 is one definition. The causal relation, the factor, the participant relation and the causal chain of each macroevent, (136), are the primitives of a Model; the thesis takes the causal relation to be Lewis's counterfactual causation and leaves its characterization open. Events are partially ordered by causal precedence, the initial event of a chain is its least event, and the Onset Condition is [Kim24]'s, Kim2024.OnsetCondition. The model of (136) draws the chain as a relation of immediate causation (SinkingEvent.Causes), ordered by its reflexive transitive closure, so the macroevent, no link in the chain, is unordered with respect to its subevents. Temporal traces are rational intervals. The compounds are entries of Fragments/Mandarin/Resultatives.lean, which record no orientation: the apparent subject-oriented transitives chī-bǎo (3) and qí-lèi (330) are the hybrid resultatives of chapter 4, whose postverbal phrase is an argument of V2, and that chapter, the V-de construction's syntax (chapter 6), the case against the No Argument Theory (chapter 5) and the null head ∅+C+B for adjectival X (693) are not formalized.

References #

The null affix (chapter 2, section 3.3) #

structure Tay2024.Model (E : Type u_3) (D : Type u_4) :
Type (max u_3 u_4)

The causal vocabulary of the null affix. cause e e₁ e₂ says the macroevent e contains the causing event e₁ and the caused event e₂; ccf e is the crucial contributory factor of e, the essential factor in bringing about its result, if e is a change with one, CCF(e) = c in (111); participant e x says x is a participant in e; and chain e is the causal chain of events that the macroevent e comprises (136).

  • cause : E → E → E → Prop
  • ccf : E → Option D
  • participant : E → D → Prop
  • chain : E → Set E
Instances For
    def Tay2024.nullAffix {E : Type u_1} {D : Type u_2} {m n : ℕ} (M : Model E D) (R2 : E → (Fin n → D) → Prop) (R1 : E → (Fin m → D) → Prop) (e : E) (ys : Fin n → D) :

    The null affix (110) introduces a macroevent e containing a causing event e₁ described by V1, whose arguments are existentially closed, and a caused event e₂ described by V2, whose arguments the compound inherits.

    Equations
    • Tay2024.nullAffix M R2 R1 e ys = ∃ (e₁ : E) (e₂ : E) (xs : Fin m → D), M.cause e e₁ e₂ ∧ R2 e₂ ys ∧ R1 e₁ xs
    Instances For
      def Tay2024.nullAffixC {E : Type u_1} {D : Type u_2} {m n : ℕ} (M : Model E D) (R2 : E → (Fin n → D) → Prop) (R1 : E → (Fin m → D) → Prop) (e : E) (c : D) (ys : Fin n → D) :

      The null affix ∅+C (111) also names the crucial contributory factor of the macroevent, which is an argument of the macroevent alone and enters no relation with the arguments of V1.

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        theorem Tay2024.nullAffix_of {E : Type u_1} {D : Type u_2} {m n : ℕ} {M : Model E D} {R2 : E → (Fin n → D) → Prop} {R1 : E → (Fin m → D) → Prop} {e e₁ e₂ : E} {ys : Fin n → D} {xs : Fin m → D} (hc : M.cause e e₁ e₂) (h2 : R2 e₂ ys) (h1 : R1 e₁ xs) :
        nullAffix M R2 R1 e ys

        Any arguments of V1 witness the compound, so nothing requires the compound's arguments to be interpreted as arguments of V1, and nothing forbids it, (131)–(134), (202)–(206).

        theorem Tay2024.nullAffix_of_agent {E : Type u_1} {D : Type u_2} {M : Model E D} {e e₁ e₂ : E} {R2 R1 : E → (Fin 1 → D) → Prop} {y : D} (hc : M.cause e e₁ e₂) (h2 : R2 e₂ ![y]) (h1 : R1 e₁ ![y]) :
        nullAffix M R2 R1 e ![y]

        The sole argument of an unaccusative compound may be the agent of V1 (219), so a subject-oriented resultative needs no reflexive.

        theorem Tay2024.ccf_unique {E : Type u_1} {D : Type u_2} {m n : ℕ} {M : Model E D} {R2 : E → (Fin n → D) → Prop} {R1 : E → (Fin m → D) → Prop} {e : E} {c c' : D} {ys : Fin n → D} {n' m' : ℕ} {R2' : E → (Fin n' → D) → Prop} {R1' : E → (Fin m' → D) → Prop} {ys' : Fin n' → D} (h : nullAffixC M R2 R1 e c ys) (h' : nullAffixC M R2' R1' e c' ys') :
        c = c'

        A change has one crucial contributory factor (chapter 8, section 3.3): two transitive compounds describing the same macroevent name the same external argument.

        The Onset Condition (chapter 3, section 2.2) #

        def Tay2024.Model.Onset {E : Type u_1} {D : Type u_2} {M : Model E D} [PartialOrder E] :

        The Onset Condition of [Kim24], (141): the causing event integrated into the macroevent of a simplex causative is the initial event of the macroevent's causal chain.

        Equations
        Instances For
          def Tay2024.Model.CcfInitial {E : Type u_1} {D : Type u_2} {M : Model E D} [PartialOrder E] :

          The crucial contributory factor is essential in bringing about the result, so it is a participant in the initial event of the causal chain (145).

          Equations
          Instances For
            theorem Tay2024.participant_of_nullAffixC {E : Type u_1} {D : Type u_2} {m n : ℕ} {M : Model E D} {R2 : E → (Fin n → D) → Prop} {R1 : E → (Fin m → D) → Prop} {e : E} {c : D} {ys : Fin n → D} [PartialOrder E] (hO : Model.Onset) (hI : Model.CcfInitial) (h : nullAffixC M R2 R1 e c ys) :
            ∃ (e₁ : E) (xs : Fin m → D), R1 e₁ xs ∧ M.participant e₁ c

            No pure causers: the external argument of a transitive compound is a participant in the event described by V1, (146)–(149), as its subject matter in (150)–(151).

            The causal chain of chén 'sink', (136)–(140) #

            The events of (136): the Russians strike the cruiser with a missile, seawater rushes into it, it descends into the water, and it is below the surface of the sea; and the macroevent of sinking that comprises them, which chén 'sink' denotes.

            Instances For
              @[instance_reducible]
              Equations

              The arrows of (136). The macroevent is no link in the chain, so it neither precedes nor follows its subevents.

              Equations
              • One or more equations did not get rendered due to their size.
              Instances For
                @[instance_reducible]
                Equations
                • One or more equations did not get rendered due to their size.

                (137)–(138): in jī-chén 'strike-sink' V1 names the striking, the onset of the chain, so the Onset Condition is met.

                (139)–(140): in *chōng-chén 'rush-sink' V1 would name the seawater rushing in, downstream of the striking, so it cannot be the integrated event.

                The participants of (135)–(140).

                Instances For
                  @[instance_reducible]
                  Equations

                  The model of (136) on which V1 names the event v1: the sinking contains v1 as its causing event and the cruiser's being below the surface as its caused event, and its crucial contributory factor is the Russian forces, who take part in the striking.

                  Equations
                  • One or more equations did not get rendered due to their size.
                  Instances For

                    On every model the factor takes part in the initial event of the chain, the striking.

                    jī-chén satisfies the Onset Condition.

                    *chōng-chén violates it.

                    def Tay2024.ji (e : SinkingEvent) (xs : Fin 2 → Participant) :

                    jī 'strike' and chén 'sink' on the events of (136).

                    Equations
                    Instances For
                      def Tay2024.chen (e : SinkingEvent) (ys : Fin 1 → Participant) :

                      jī 'strike' and chén 'sink' on the events of (136).

                      Equations
                      Instances For

                        (137) through the whole pipeline: Éjūn jī-chén-le yī sōu xúnyángjiàn denotes the sinking, and the Onset Condition puts the Russian forces in the event V1 describes.

                        The external argument in the data (chapter 3, sections 2.1–2.2) #

                        The paper's reading of the external argument of a transitive compound relative to V1.

                        Instances For
                          @[instance_reducible]
                          Equations

                          The reading of the external argument a row records.

                          Equations
                          • One or more equations did not get rendered due to their size.
                          Instances For

                            A transitive compound is ungrammatical exactly where its external argument is a pure causer, as participant_of_nullAffixC predicts.

                            Trieventive structure (chapter 2, section 3.3) #

                            def Tay2024.Monoeventive {E : Type u_1} (trace : E → Set ℚ) (e₁ e₂ : E) :

                            The temporal signature of the monoeventive analysis (104): V1 and V2 describe one event, so one trace.

                            Equations
                            Instances For
                              def Tay2024.Bieventive {E : Type u_1} (trace : E → Set ℚ) (e₁ e₂ : E) :

                              The temporal signature of the bieventive analyses (105)–(106): one event is a part of the other, so one trace contains the other.

                              Equations
                              • Tay2024.Bieventive trace e₁ e₂ = (trace e₂ ⊆ trace e₁ ∨ trace e₁ ⊆ trace e₂)
                              Instances For
                                inductive Tay2024.Ev :

                                The events of shè-sǐ 'shoot dead' (107).

                                Instances For
                                  def Tay2024.shooting :
                                  Ev → Set ℚ

                                  In the traces of (108) the shooting ends as the bullet makes contact, when the dying begins.

                                  Equations
                                  Instances For

                                    The shooting and the dying overlap at a single point, so they are neither one event nor nested, so only the trieventive macroevent accounts for (107).

                                    The compound in morphology (chapter 2, section 2) #

                                    The null affix as a morph is a phonologically empty prefix on V2.

                                    Equations
                                    Instances For

                                      The word V1-∅-V2 (130): ∅ affixed to V2, the result compounded with V1.

                                      Equations
                                      Instances For
                                        @[simp]
                                        theorem Tay2024.toList_vvTree (v1 v2 : Morphology.Morph) :
                                        (vvTree v1 v2).toList = [v1, nullMorph, v2]

                                        The word V1-∅-V2 of a compound of the fragment.

                                        Equations
                                        Instances For

                                          The word differs from the fragment's root compound by the null affix alone.

                                          Typology (chapter 8) #

                                          The parameters of the typology: whether the null head merges in morphology and whether the result X can be a verb (section 2), and whether the language's deadjectival change-of-state verbs have transitive counterparts (section 3.1), in which case its intransitive change-of-state verbs are reflexivizations carrying their own crucial contributory factor (692), and otherwise denote a becoming with none (686).

                                          • compound : Bool
                                          • verbalX : Bool
                                          • alternating : Bool
                                          Instances For

                                            A transitive resultative takes an intransitive X iff X can be a verb that carries no factor, so that the null head ∅+C supplies one (694), (697); an X carrying its own leaves none for the head to introduce, since a change has one (section 3.3).

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                                              Mandarin V-V resultatives are compounds with a verbal X, and its deadjectival change-of-state verbs lack transitive counterparts (681)–(683), so a transitive resultative takes an intransitive X, dǎ-pò (673).

                                              Equations
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                                                English resultatives are not compounds, X is never a verb (669), and break alternates (676)–(677).

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                                                  Japanese V-V resultatives are compounds with a verbal X, and its change-of-state verbs come in transitive and unaccusative pairs (687)–(690), so a transitive resultative takes no intransitive X (674)–(675).

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                                                    pò 'break' has no transitive frame (684)–(685), the datum behind Mandarin's parameter.