Henderson and Coon (2018): Adverbs and variability in Kaqchikel Agent Focus

Erlewine derives the Kaqchikel ban on extracting a transitive subject from anti-locality: the subject sits in Spec,IP, one step below Spec,CP, so an adverb adding a projection between them should make Agent Focus unnecessary. Henderson and Coon reply that a subject extracts with ergative agreement and no Agent Focus when its object is a reflexive, an extended reflexive, a clause or a light verb's complement, as accounts on which the object's Case traps the subject expect, and that the adverb effect is not one: the same adverb occurs with Agent Focus and without it, negation never removes it, and adverbs that cannot take a clause never do. A string without Agent Focus is biclausal, an adverb predicated of a clause whose subject is a resumptive pronoun, so nothing is extracted; an overt complementizer or pronoun forces that parse, and Agent Focus then appears only when the pronoun is focused inside the lower clause.

Main statements

• rows_fit: with the two parses and a case-based account of extraction, every example is grammatical exactly when one of its parses converges.
• monoclausal_fits_iff: with the monoclausal parse alone the case-based account fails exactly on the examples without Agent Focus whose subject seems to cross an adverb that takes a clause.
• antiLocality_fits_iff: Erlewine's grammar fits an example exactly when its object is a full DP and either nothing intervenes or a transitive verb follows an adverb that takes a clause.

Implementation notes

• The case-based account is the convergence of Studies/CoonMateoPedroPreminger2014.lean with Infl licensing the object, as Kaqchikel's high absolutive has it. Henderson and Coon endorse no particular account of this kind, and that one was proposed for Q'anjob'al.
• Reflexive and extended reflexive objects are caseless, as in that study; the clausal complement and the light verb's complement are taken to need no Case either, the explanation Henderson and Coon suggest.
• The biclausal parse is available when the intervener is an adverb that takes a clause, the monoclausal parse when no overt complementizer or resumptive pronoun marks a lower clause. Erlewine's grammar reads any intervener, negation included, as one projection above TP.
• Example numbers are the published version's. The examples are Data.Examples.HendersonCoon2018; the attested (26), whose object may be a clause, and (44), whose verb is a perfect, are left out.

References

• [HC18]
• [Erl16]
• [CMPP14]

Interveners

inductive HendersonCoon2018.Intervener : Type

The material between a preverbal phrase and the verb, the adverbs kan qitzij and kan 'truly', k'a ri 'then', jantäq 'sometimes' and jumul 'always', and negation man.

• kanQitzij : Intervener
• kan : Intervener
• k'aRi : Intervener
• jantäq : Intervener
• jumul : Intervener
• negation : Intervener

@[instance_reducible]

instance HendersonCoon2018.instDecidableEqIntervener : DecidableEq Intervener

Equations

• HendersonCoon2018.instDecidableEqIntervener x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance HendersonCoon2018.instReprIntervener : Repr Intervener

Equations

• HendersonCoon2018.instReprIntervener = { reprPrec := HendersonCoon2018.instReprIntervener.repr }

def HendersonCoon2018.instReprIntervener.repr : Intervener → ℕ → Std.Format

Equations

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

def HendersonCoon2018.Intervener.TakesClause (i : Intervener) : Prop

An intervener can be a predicate taking a clause, as kan qitzij, kan and k'a ri can (§5.1) and jantäq, jumul (§5.3) and negation (§4) cannot.

Equations

• i.TakesClause = (i = HendersonCoon2018.Intervener.kanQitzij ∨ i = HendersonCoon2018.Intervener.kan ∨ i = HendersonCoon2018.Intervener.k'aRi)

@[instance_reducible]

instance HendersonCoon2018.instDecidablePredIntervenerTakesClause : DecidablePred Intervener.TakesClause

Equations

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Examples and their parses

inductive HendersonCoon2018.ObjectKind : Type

The objects of §3.2.

• dp : ObjectKind
• reflexive : ObjectKind
• extendedReflexive : ObjectKind
• clause : ObjectKind
• lightVerb : ObjectKind

@[instance_reducible]

instance HendersonCoon2018.instDecidableEqObjectKind : DecidableEq ObjectKind

Equations

• HendersonCoon2018.instDecidableEqObjectKind x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance HendersonCoon2018.instReprObjectKind : Repr ObjectKind

Equations

• HendersonCoon2018.instReprObjectKind = { reprPrec := HendersonCoon2018.instReprObjectKind.repr }

def HendersonCoon2018.instReprObjectKind.repr : ObjectKind → ℕ → Std.Format

Equations

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

def HendersonCoon2018.ObjectKind.toObject : ObjectKind → CoonMateoPedroPreminger2014.Object

The case-based account's object: a full DP needs Case and the others are caseless.

Equations

• HendersonCoon2018.ObjectKind.dp.toObject = CoonMateoPedroPreminger2014.Object.dp
• x✝.toObject = CoonMateoPedroPreminger2014.Object.caseless

inductive HendersonCoon2018.Resumption : Type

What stands where an extracted subject would leave its trace, a gap, an overt resumptive pronoun, or one focused inside its clause.

• gap : Resumption
• pronoun : Resumption
• focused : Resumption

@[instance_reducible]

instance HendersonCoon2018.instDecidableEqResumption : DecidableEq Resumption

Equations

• HendersonCoon2018.instDecidableEqResumption x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance HendersonCoon2018.instReprResumption : Repr Resumption

Equations

• HendersonCoon2018.instReprResumption = { reprPrec := HendersonCoon2018.instReprResumption.repr }

def HendersonCoon2018.instReprResumption.repr : Resumption → ℕ → Std.Format

Equations

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

structure HendersonCoon2018.Example : Type

An extraction example, with the argument that seems extracted, the form of the verb, the object, what intervenes, whether a complementizer is overt, what stands at the subject position, and the persons of the arguments.

• extracted : Erlewine2016.Arg
• form : Mayan.VerbForm
• object : ObjectKind
• intervener : Option Intervener
• complementizer : Bool
• resumption : Resumption
• subject : Person
• objectPerson : Person

inductive HendersonCoon2018.Parse : Type

The two structures a string may have (§5), one clause with its phrase extracted past the intervener, or an adverb predicated of a lower clause with a resumptive subject.

• monoclausal : Parse
• biclausal : Parse

@[instance_reducible]

instance HendersonCoon2018.instDecidableEqParse : DecidableEq Parse

Equations

• HendersonCoon2018.instDecidableEqParse x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance HendersonCoon2018.instFintypeParse : Fintype Parse

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@[instance_reducible]

instance HendersonCoon2018.instReprParse : Repr Parse

Equations

• HendersonCoon2018.instReprParse = { reprPrec := HendersonCoon2018.instReprParse.repr }

def HendersonCoon2018.instReprParse.repr : Parse → ℕ → Std.Format

Equations

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

def HendersonCoon2018.Example.Parses (e : Example) : Parse → Prop

A string parses as one clause unless an overt complementizer or resumptive pronoun marks a lower clause, and as two when the intervener takes a clause.

Equations

• e.Parses HendersonCoon2018.Parse.monoclausal = (e.complementizer = false ∧ e.resumption = HendersonCoon2018.Resumption.gap)
• e.Parses HendersonCoon2018.Parse.biclausal = ∃ i ∈ e.intervener, i.TakesClause

@[instance_reducible]

instance HendersonCoon2018.Example.instDecidablePredParseParses (e : Example) : DecidablePred e.Parses

Equations

• One or more equations did not get rendered due to their size.
• e.instDecidablePredParseParses HendersonCoon2018.Parse.biclausal = HendersonCoon2018.Example.instDecidablePredParseParses._aux_2 e

def HendersonCoon2018.Example.extractedRole (e : Example) : Parse → Option ArgumentRole

The role extracted in a parse's clause, the phrase itself in one clause and, in the lower clause of two, only a focused resumptive pronoun.

Equations

• e.extractedRole HendersonCoon2018.Parse.monoclausal = some (Erlewine2016.Arg.role true e.extracted)
• e.extractedRole HendersonCoon2018.Parse.biclausal = if e.resumption = HendersonCoon2018.Resumption.focused then some (Erlewine2016.Arg.role true e.extracted) else none

def HendersonCoon2018.Example.clause (e : Example) (p : Parse) : CoonMateoPedroPreminger2014.Clause

The clause the case-based account judges for a parse: finite, Infl licensing the object, the Voice of the attested form and the object's Case needs.

Equations

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

def HendersonCoon2018.Example.erlewineInput (e : Example) : Erlewine2016.Input

Erlewine's input for the string as one clause, any intervener a projection above TP below the landing site.

Equations

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def HendersonCoon2018.Example.AntiLocality (e : Example) : Prop

Erlewine's grammar realizes the attested form in an optimal derivation.

Equations

• e.AntiLocality = ∃ c ∈ (Erlewine2016.kaqchikel.tableau e.erlewineInput).optimal, Erlewine2016.Candidate.form e.erlewineInput.args c = e.form

@[instance_reducible]

instance HendersonCoon2018.Example.instDecidableAntiLocality (e : Example) : Decidable e.AntiLocality

Equations

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

The examples

def HendersonCoon2018.intervenerTable : List (String × Intervener)

The rows' labels for the interveners.

Equations

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

def HendersonCoon2018.objectTable : List (String × ObjectKind)

The rows' labels for the objects.

Equations

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

def HendersonCoon2018.Example.ofDatum (d : Datum) : Option Example

The example an extraction row describes.

Equations

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

def HendersonCoon2018.IsExtraction (d : Datum) : Prop

An extraction row.

Equations

• HendersonCoon2018.IsExtraction d = (d.feature? "construction" = some "extraction")

@[instance_reducible]

instance HendersonCoon2018.instDecidablePredDatumIsExtraction : DecidablePred IsExtraction

Equations

• HendersonCoon2018.instDecidablePredDatumIsExtraction x✝ = HendersonCoon2018.instDecidablePredDatumIsExtraction._aux_1 x✝

theorem HendersonCoon2018.rows_fit (d : Datum) : d ∈ Examples.all → IsExtraction d → ∃ e ∈ Example.ofDatum d, d.judgment = Judgment.acceptable ↔ ∃ (p : Parse), e.Parses p ∧ CoonMateoPedroPreminger2014.Converges (e.clause p)

Every example is grammatical exactly when one of its parses converges under the case-based account (§5): Agent Focus where a subject is extracted in its own clause, the transitive form where it is not, past an adverb taking a clause or a caseless object.

theorem HendersonCoon2018.monoclausal_fits_iff (d : Datum) : d ∈ Examples.all → IsExtraction d → ∃ e ∈ Example.ofDatum d, e.Parses Parse.monoclausal → ((d.judgment = Judgment.acceptable ↔ CoonMateoPedroPreminger2014.Converges (e.clause Parse.monoclausal)) ↔ ¬(e.form = Mayan.VerbForm.transitive ∧ e.extracted = Erlewine2016.Arg.subj ∧ ∃ i ∈ e.intervener, i.TakesClause))

Without the biclausal parse the case-based account fails exactly on the examples without Agent Focus whose subject seems to cross an adverb that takes a clause, the minimal pairs of §4; the examples with an overt complementizer or pronoun have no other parse.

theorem HendersonCoon2018.antiLocality_fits_iff (d : Datum) : d ∈ Examples.all → IsExtraction d → ∃ e ∈ Example.ofDatum d, e.Parses Parse.monoclausal → ((d.judgment = Judgment.acceptable ↔ e.AntiLocality) ↔ e.object = ObjectKind.dp ∧ (e.intervener = none ∨ e.form = Mayan.VerbForm.transitive ∧ ∃ i ∈ e.intervener, i.TakesClause))

Erlewine's grammar fits an example read as one clause exactly when its object is a full DP and either nothing intervenes or a transitive verb follows an adverb that takes a clause. It misses the caseless objects of §3.2, Agent Focus past any adverb, negation, and the adverbs that take no clause (§4, §5.3), and since its outcome is fixed by the input it cannot give both forms past the same adverb, as (5) and (6) have.

theorem HendersonCoon2018.embedding_rows (d : Datum) : d ∈ Examples.all → d.feature? "construction" = some "embedding" → ∃ i ∈ d.parse? "adverb" intervenerTable, d.judgment = Judgment.acceptable ↔ i.TakesClause

The adverbs that take a clause in the embedding examples are those Intervener.TakesClause names (§5.1, §5.3).