Koontz-Garboden (2009): Anticausativization

Koontz-Garboden analyzes anticausativization, the derivation of an inchoative from its causative as in Spanish romper 'break (tr.)' ~ romperse 'break (intr.)', as reflexivization. The reflexive clitic denotes Chierchia's operator λℜλx[ℜ(x,x)], so a derived inchoative is its causative restricted to the diagonal and keeps the CAUSE operator: its single argument causes its own change. A verb whose causer must be an agent, like asesinar 'assassinate', therefore reflexivizes only to a reflexive reading, while a verb with Van Valin and Wilkins's underspecified EFFECTOR, like romper, also has the anticausative reading. Por sí solo 'by itself' is licensed by derived inchoatives but not by passives or by the CAUSE-less representation of internally caused verbs. Unlike Grimshaw's inchoativization rule, which strips CAUSE, reflexivization respects the Monotonicity Hypothesis that word formation never removes operators.

Main definitions

• anticausative: the derived inchoative, the causative on its diagonal.
• AnticausativeReading: the anticausative reading of a reflexivized verb.
• LicensesBySelf: the licensing condition of por sí solo.
• MonotonicityHypothesis: the Monotonicity Hypothesis on event templates.

Main results

• exists_cause_of_anticausative: CAUSE survives reflexivization.
• not_anticausativeReading: an agent-causer verb has no anticausative reading.
• licensesBySelf_anticausative: derived inchoatives license por sí solo.
• not_monotonicityHypothesis_caused: inchoativization violates the hypothesis.
• monotonicityHypothesis_reflexivizeTemplate: reflexivization satisfies it.

Implementation notes

The paper's representations take the change-of-state event as the verb's event argument and existentially close the causing event; causative follows that convention, and exists_causative_iff shows that its existential closure agrees with the library's causative head vCause, whose event argument is the causing event. Agent entailments are an explicit relation on the model, since EventStructure.Interpretation has only the underspecified effector. A Spanish verb's causer specification is derived from the proto-role subject profile the fragment states for it, after Dowty: a causer that must be an agent entails volition. The reflexive/anticausative syncretism in Haspelmath's survey, which the paper tabulates, is a typological argument left in prose.

References

• [KG09]
• [Chi04a]
• [VVW96]
• [Gri82]
• [RS05]
• [LRH95]
• [RHL98]
• [Dow91]
• [Has90]

def KoontzGarboden2009.reflexivize {α : Type u_1} {β : Type u_2} (R : α → α → β) : α → β

The reflexivization operator restricts a two-place relation to its diagonal. It is the denotation of the reflexive clitic se.

Equations

• KoontzGarboden2009.reflexivize R x = R x x

def KoontzGarboden2009.causative {Entity : Type u_1} {State : Type u_2} {E : Type u_3} (M : ArgumentStructure.EventStructure.Interpretation Entity State E) (θ : Entity → E → Prop) (P : Entity → State → Prop) (y x : Entity) (e : E) : Prop

A causative change-of-state verb, ((10b), (17), (29)), holds of an event e in which x comes to be in the root's state, caused by an event whose participant y bears the causer relation θ, the underspecified M.effector for romper and an agent relation for asesinar.

Equations

• KoontzGarboden2009.causative M θ P y x e = ∃ (w : E), θ y w ∧ M.cause w e ∧ M.vBecome P x e

theorem KoontzGarboden2009.exists_causative_iff {Entity : Type u_1} {State : Type u_2} {E : Type u_3} (M : ArgumentStructure.EventStructure.Interpretation Entity State E) (P : Entity → State → Prop) (y x : Entity) : (∃ (e : E), causative M M.effector P y x e) ↔ ∃ (w : E), M.vCause (M.vBecome P x) y w

Over the underspecified causer, causative and the head vCause over vBecome have the same existential closure; they differ only in which event is the verb's argument.

def KoontzGarboden2009.anticausative {Entity : Type u_1} {State : Type u_2} {E : Type u_3} (M : ArgumentStructure.EventStructure.Interpretation Entity State E) (θ : Entity → E → Prop) (P : Entity → State → Prop) : Entity → E → Prop

Anticausativization is reflexivization. The derived inchoative is the causative on its diagonal, so the undergoer is also the participant in the causing event.

Equations

• KoontzGarboden2009.anticausative M θ P = KoontzGarboden2009.reflexivize (KoontzGarboden2009.causative M θ P)

theorem KoontzGarboden2009.anticausative_iff {Entity : Type u_1} {State : Type u_2} {E : Type u_3} (M : ArgumentStructure.EventStructure.Interpretation Entity State E) (θ : Entity → E → Prop) (P : Entity → State → Prop) (x : Entity) (e : E) : anticausative M θ P x e ↔ ∃ (w : E), θ x w ∧ M.cause w e ∧ M.vBecome P x e

def KoontzGarboden2009.AnticausativeReading {Entity : Type u_1} {State : Type u_2} {E : Type u_3} (M : ArgumentStructure.EventStructure.Interpretation Entity State E) (agent P : Entity → E → Prop) : Prop

A reflexivized verb has the anticausative reading when it has an instance whose single argument is not an agent of the event causing its change, as in el vaso se rompió 'the cup broke'.

Equations

• KoontzGarboden2009.AnticausativeReading M agent P = ∃ (x : Entity) (e : E), P x e ∧ ∀ (w : E), M.cause w e → ¬agent x w

def KoontzGarboden2009.LicensesBySelf {Entity : Type u_1} {State : Type u_2} {E : Type u_3} (M : ArgumentStructure.EventStructure.Interpretation Entity State E) (P : Entity → E → Prop) : Prop

Por sí solo 'by itself' ((54)) is licensed on a predicate that entails a causing subevent with the subject as its effector; the modifier then adds that the subject is its sole effector (§3.4, §4.1).

Equations

• KoontzGarboden2009.LicensesBySelf M P = ∀ (x : Entity) (e : E), P x e → ∃ (w : E), M.cause w e ∧ M.effector x w

def KoontzGarboden2009.passive {Entity : Type u_1} {State : Type u_2} {E : Type u_3} (M : ArgumentStructure.EventStructure.Interpretation Entity State E) (P : Entity → State → Prop) (x : Entity) (e : E) : Prop

In the passive of a causative verb the causer is existentially closed rather than identified with the subject.

Equations

• KoontzGarboden2009.passive M P x e = ∃ (y : Entity), KoontzGarboden2009.causative M M.effector P y x e

theorem KoontzGarboden2009.causative_self_of_anticausative {Entity : Type u_1} {State : Type u_2} {E : Type u_3} {M : ArgumentStructure.EventStructure.Interpretation Entity State E} {θ : Entity → E → Prop} {P : Entity → State → Prop} {x : Entity} {e : E} (h : anticausative M θ P x e) : causative M θ P x x e

A derived inchoative entails the causative with its subject as its own causer, the special kind of causative that §3.5 finds the inchoative to entail.

theorem KoontzGarboden2009.exists_cause_of_anticausative {Entity : Type u_1} {State : Type u_2} {E : Type u_3} {M : ArgumentStructure.EventStructure.Interpretation Entity State E} {θ : Entity → E → Prop} {P : Entity → State → Prop} {x : Entity} {e : E} (h : anticausative M θ P x e) : ∃ (w : E), θ x w ∧ M.cause w e

A derived inchoative retains a causing subevent whose causer is its subject, so CAUSE survives reflexivization.

theorem KoontzGarboden2009.exists_nonagent_of_anticausativeReading {Entity : Type u_1} {State : Type u_2} {E : Type u_3} {M : ArgumentStructure.EventStructure.Interpretation Entity State E} {θ agent : Entity → E → Prop} {P : Entity → State → Prop} (h : AnticausativeReading M agent (anticausative M θ P)) : ∃ (x : Entity) (w : E), θ x w ∧ ¬agent x w

Only verbs with a thematically underspecified causer anticausativize, since an anticausative reading needs a causer relation satisfied by a non-agent.

theorem KoontzGarboden2009.not_anticausativeReading {Entity : Type u_1} {State : Type u_2} {E : Type u_3} {M : ArgumentStructure.EventStructure.Interpretation Entity State E} {θ agent : Entity → E → Prop} {P : Entity → State → Prop} (hθ : ∀ (x : Entity) (w : E), θ x w → agent x w) : ¬AnticausativeReading M agent (anticausative M θ P)

A verb whose causer must be an agent ((29), asesinar) reflexivizes to the reflexive-type reading only ((27)–(28), (31)).

theorem KoontzGarboden2009.licensesBySelf_anticausative {Entity : Type u_1} {State : Type u_2} {E : Type u_3} {M : ArgumentStructure.EventStructure.Interpretation Entity State E} {P : Entity → State → Prop} : LicensesBySelf M (anticausative M M.effector P)

Derived inchoatives license por sí solo ((68)).

Juan and the glass

The model of (56)–(57) and (60) has Juan break the glass. Whether the glass counts as an effector of the causing event is a parameter; the denial in (56) has it that it does not, the discourse in (60) that both the glass and Juan do.

inductive KoontzGarboden2009.Participant : Type

A Participant is one of the participants of the models.

• juan : Participant
• vaso : Participant

@[instance_reducible]

instance KoontzGarboden2009.instDecidableEqParticipant : DecidableEq Participant

Equations

• KoontzGarboden2009.instDecidableEqParticipant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def KoontzGarboden2009.breaking (eff : Participant → Prop) : ArgumentStructure.EventStructure.Interpretation Participant Unit Unit

In the model where Juan breaks the glass, eff says who counts as an effector of the causing event, and every event gives rise to the glass's broken state.

Equations

• KoontzGarboden2009.breaking eff = { become := fun (x x_1 : Unit) => True, cause := fun (x x_1 : Unit) => True, effector := fun (y : KoontzGarboden2009.Participant) (x : Unit) => eff y }

def KoontzGarboden2009.broken (x : Participant) : Unit → Prop

The broken state holds of the glass.

Equations

• KoontzGarboden2009.broken x x✝ = (x = KoontzGarboden2009.Participant.vaso)

def KoontzGarboden2009.juanAgent (y : Participant) : Unit → Prop

Juan alone is an agent.

Equations

• KoontzGarboden2009.juanAgent y x✝ = (y = KoontzGarboden2009.Participant.juan)

def KoontzGarboden2009.breakingByJuan : ArgumentStructure.EventStructure.Interpretation Participant Unit Unit

In the first model Juan, not the glass, is the effector.

Equations

• KoontzGarboden2009.breakingByJuan = KoontzGarboden2009.breaking fun (x : KoontzGarboden2009.Participant) => x = KoontzGarboden2009.Participant.juan

def KoontzGarboden2009.breakingByBoth : ArgumentStructure.EventStructure.Interpretation Participant Unit Unit

In the second model the glass and Juan are both effectors.

Equations

• KoontzGarboden2009.breakingByBoth = KoontzGarboden2009.breaking fun (x : KoontzGarboden2009.Participant) => True

def KoontzGarboden2009.e₀ : Unit

e₀ is the one event of the models.

Equations

• KoontzGarboden2009.e₀ = ()

theorem KoontzGarboden2009.not_anticausative_of_causative : causative breakingByJuan breakingByJuan.effector broken Participant.juan Participant.vaso e₀ ∧ ¬anticausative breakingByJuan breakingByJuan.effector broken Participant.vaso e₀

The causative does not entail the derived inchoative. With Juan the only effector, Juan rompió el vaso holds and el vaso se rompió fails.

theorem KoontzGarboden2009.anticausativeReading_romper : AnticausativeReading breakingByBoth juanAgent (anticausative breakingByBoth breakingByBoth.effector broken)

El vaso se rompió has the anticausative reading, the glass being a non-agentive effector of its own breaking.

theorem KoontzGarboden2009.not_licensesBySelf_passive : ¬LicensesBySelf breakingByJuan (passive breakingByJuan broken)

A passive does not license por sí solo, since its subject need not be an effector of the causing subevent.

theorem KoontzGarboden2009.not_licensesBySelf_inchoative : ¬LicensesBySelf breakingByJuan (breakingByJuan.vBecome broken)

The CAUSE-less representation of an internally caused verb ((65), (67)), the head vBecome alone, does not license por sí solo.

The Monotonicity Hypothesis

def KoontzGarboden2009.MonotonicityHypothesis (f : ArgumentStructure.EventStructure.Template ArgumentStructure.EventStructure.Eventuality.event → Option (ArgumentStructure.EventStructure.Template ArgumentStructure.EventStructure.Eventuality.event)) : Prop

The Monotonicity Hypothesis (8) holds of a word formation operation on event templates when the output keeps every kind of operator the input has.

Equations

• KoontzGarboden2009.MonotonicityHypothesis f = ∀ (t t' : ArgumentStructure.EventStructure.Template ArgumentStructure.EventStructure.Eventuality.event), f t = some t' → t.kinds ⊆ t'.kinds

theorem KoontzGarboden2009.not_monotonicityHypothesis_caused : ¬MonotonicityHypothesis ArgumentStructure.EventStructure.Template.caused

The inchoativization rule of [Gri82] ((95)) keeps the caused subevent, stripping CAUSE and the causing subevent from an accomplishment; it violates the hypothesis.

def KoontzGarboden2009.reflexivizeTemplate (t : ArgumentStructure.EventStructure.Template ArgumentStructure.EventStructure.Eventuality.event) : Option (ArgumentStructure.EventStructure.Template ArgumentStructure.EventStructure.Eventuality.event)

Reflexivization on templates identifies the causer with the undergoer, so it applies exactly to templates with CAUSE and changes no operator.

Equations

• KoontzGarboden2009.reflexivizeTemplate t = if t.HasCause then some t else none

theorem KoontzGarboden2009.monotonicityHypothesis_reflexivizeTemplate : MonotonicityHypothesis reflexivizeTemplate

Anticausativization as reflexivization satisfies the hypothesis.

Spanish verbs

inductive KoontzGarboden2009.Causer : Type

The thematic specification of a verb's causer is an underspecified EFFECTOR or an AGENT.

• effector : Causer
• agent : Causer

@[instance_reducible]

instance KoontzGarboden2009.instDecidableEqCauser : DecidableEq Causer

Equations

• KoontzGarboden2009.instDecidableEqCauser x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance KoontzGarboden2009.instReprCauser : Repr Causer

Equations

• KoontzGarboden2009.instReprCauser = { reprPrec := KoontzGarboden2009.instReprCauser.repr }

def KoontzGarboden2009.instReprCauser.repr : Causer → ℕ → Std.Format

Equations

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

def KoontzGarboden2009.causer (v : Verb) : Option Causer

A verb's causer specification is derived from its stated proto-role subject profile. A causer that must be an agent entails volition, one that need only cause the change is an EFFECTOR, and a subject that causes nothing is no causer.

Equations

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

theorem KoontzGarboden2009.alternates_iff_effector (v : Spanish.Verbs.SpanishVerbEntry) : v ∈ Spanish.Verbs.allVerbs → ∀ c ∈ causer v.toVerb, v.Alternates ↔ c = Causer.effector

Only causative verbs with underspecified causers have derived inchoatives (§3.1–§3.2), so among the fragment's verbs that have a causer, the alternating ones are the EFFECTOR verbs.