Anderson 2006: localist case grammar

Every semantic relation an argument bears is a bundle of the three first-order case features of chapter 6 — absolutive, the semantically empty relation; source, whose non-locational form is the ergative; and locative, which may carry source or goal as a second-order feature — and all eight combinations occur: the Experiencer is a locative source, the contactive patient an absolutive locative, and suffer's subject bears all three. Subject selection ranks ergative above ergative absolutive above absolutive, so only a non-spatial source or an absolutive can be subject, and subject formation then marks a selected absolutive as ergative — the neutralization behind subjecthood.

Main definitions

• Relation: a bundle of first-order Features (the second-order {goal} and {src} are not represented); subjectRank the hierarchy (38)′, subject the selected argument of a Predication, subjectFormation rule (40).
• andersonLinking: the hierarchy as a LinkingTheory, via Relation.toRole.

References

• [anderson-2006b]

Case features and relations

inductive Anderson2006b.Feature : Type

The three first-order case features (11).

• abs : Feature
• src : Feature
• loc : Feature

@[instance_reducible]

instance Anderson2006b.instDecidableEqFeature : DecidableEq Feature

Equations

• Anderson2006b.instDecidableEqFeature x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance Anderson2006b.instFintypeFeature : Fintype Feature

Equations

• Anderson2006b.instFintypeFeature = { elems := { val := ↑Anderson2006b.Feature.enumList, nodup := Anderson2006b.Feature.enumList_nodup }, complete := Anderson2006b.instFintypeFeature._proof_1 }

@[reducible, inline]

abbrev Anderson2006b.Relation : Type

A semantic relation is a bundle of first-order features; the eight combinations all occur (§6.2).

Equations

• Anderson2006b.Relation = Finset Anderson2006b.Feature

@[reducible, inline]

abbrev Anderson2006b.Relation.absolutive : Relation

The semantically empty relation.

Equations

• Anderson2006b.Relation.absolutive = {Anderson2006b.Feature.abs}

@[reducible, inline]

abbrev Anderson2006b.Relation.ergative : Relation

Non-locational source.

Equations

• Anderson2006b.Relation.ergative = {Anderson2006b.Feature.src}

@[reducible, inline]

abbrev Anderson2006b.Relation.locative : Relation

Equations

• Anderson2006b.Relation.locative = {Anderson2006b.Feature.loc}

@[reducible, inline]

abbrev Anderson2006b.Relation.ergAbs : Relation

The self-mover of (39c).

Equations

• Anderson2006b.Relation.ergAbs = {Anderson2006b.Feature.abs, Anderson2006b.Feature.src}

@[reducible, inline]

abbrev Anderson2006b.Relation.experiencer : Relation

The Experiencer, a locative source (39h).

Equations

• Anderson2006b.Relation.experiencer = {Anderson2006b.Feature.src, Anderson2006b.Feature.loc}

@[reducible, inline]

abbrev Anderson2006b.Relation.contactive : Relation

The contactive patient (22).

Equations

• Anderson2006b.Relation.contactive = {Anderson2006b.Feature.abs, Anderson2006b.Feature.loc}

def Anderson2006b.Relation.toRole (r : Relation) : Option ThetaRole

The hom onto the project's role labels: a locative source is an experiencer, any other source an agent, a sourceless absolutive a patient.

Equations

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

Subject selection and subject formation

def Anderson2006b.subjectRank (r : Relation) : ℕ

The subject selection hierarchy (38)′: ergative > ergative absolutive > absolutive; a purely spatial argument is ineligible, and the locative feature is irrelevant.

Equations

• Anderson2006b.subjectRank r = if Anderson2006b.Feature.src ∈ r then if Anderson2006b.Feature.abs ∈ r then 2 else 3 else if Anderson2006b.Feature.abs ∈ r then 1 else 0

theorem Anderson2006b.subjectRank_ergative_gt_ergAbs : subjectRank Relation.ergAbs < subjectRank Relation.ergative

theorem Anderson2006b.subjectRank_ergAbs_gt_absolutive : subjectRank Relation.absolutive < subjectRank Relation.ergAbs

theorem Anderson2006b.subjectRank_insert_loc (r : Relation) : subjectRank (insert Feature.loc r) = subjectRank r

theorem Anderson2006b.experiencer_ne_ergative : Relation.experiencer ≠ Relation.ergative ∧ subjectRank Relation.experiencer = subjectRank Relation.ergative

The Experiencer and the ergative differ in content but not in rank.

@[reducible, inline]

abbrev Anderson2006b.Predication : Type

The relations of a predication's arguments.

Equations

• Anderson2006b.Predication = List Anderson2006b.Relation

def Anderson2006b.subject (p : Predication) : Option Relation

The selected subject: the highest-ranked argument.

Equations

• Anderson2006b.subject p = List.argmax Anderson2006b.subjectRank p

def Anderson2006b.subjectFormation (r : Relation) : Relation

Subject formation (40): the selected argument acquires the ergative feature.

Equations

• Anderson2006b.subjectFormation r = insert Anderson2006b.Feature.src r

theorem Anderson2006b.src_mem_subjectFormation (r : Relation) : Feature.src ∈ subjectFormation r

Subject marks a non-spatial source, inherent or derived by (40).

theorem Anderson2006b.subjectFormation_eq_self {r : Relation} (h : Feature.src ∈ r) : subjectFormation r = r

An inherent source is untouched by (40): the neutralization leaves the residue the ergative subjects have in common.

The derivations of (39)

def Anderson2006b.read : Predication

Equations

• Anderson2006b.read = [Anderson2006b.Relation.ergative, Anderson2006b.Relation.absolutive]

def Anderson2006b.fell : Predication

Equations

• Anderson2006b.fell = [Anderson2006b.Relation.absolutive, Anderson2006b.Relation.locative]

def Anderson2006b.flew : Predication

Equations

• Anderson2006b.flew = [Anderson2006b.Relation.ergAbs, Anderson2006b.Relation.locative]

def Anderson2006b.knew : Predication

Equations

• Anderson2006b.knew = [Anderson2006b.Relation.experiencer, Anderson2006b.Relation.absolutive]

def Anderson2006b.suffered : Predication

Equations

• Anderson2006b.suffered = [{Anderson2006b.Feature.abs, Anderson2006b.Feature.src, Anderson2006b.Feature.loc}, Anderson2006b.Relation.locative]

theorem Anderson2006b.subjects_39 : subject read = some Relation.ergative ∧ subject fell = some Relation.absolutive ∧ subject flew = some Relation.ergAbs ∧ subject knew = some Relation.experiencer ∧ subject suffered = some {Feature.abs, Feature.src, Feature.loc}

theorem Anderson2006b.fell_subject_not_src (r : Relation) : r ∈ (subject fell).toList → Feature.src ∉ r ∧ Feature.src ∈ subjectFormation r

(39b) is the odd one out: its subject is not inherently ergative and is assimilated to the others only by (40).

The book's examples

def Anderson2006b.Relation.ofString? : String → Option Relation

The relation strings of the example rows.

Equations

• Anderson2006b.Relation.ofString? "abs" = some Anderson2006b.Relation.absolutive
• Anderson2006b.Relation.ofString? "erg" = some Anderson2006b.Relation.ergative
• Anderson2006b.Relation.ofString? "loc" = some Anderson2006b.Relation.locative
• Anderson2006b.Relation.ofString? "abs,erg" = some Anderson2006b.Relation.ergAbs
• Anderson2006b.Relation.ofString? "erg,loc" = some Anderson2006b.Relation.experiencer
• Anderson2006b.Relation.ofString? "abs,loc" = some Anderson2006b.Relation.contactive
• Anderson2006b.Relation.ofString? "abs,erg,loc" = some {Anderson2006b.Feature.abs, Anderson2006b.Feature.src, Anderson2006b.Feature.loc}
• Anderson2006b.Relation.ofString? x✝ = none

def Anderson2006b.predicationOfRow (r : Data.Examples.LinguisticExample) : Predication

The predication a row records.

Equations

• Anderson2006b.predicationOfRow r = List.filterMap (fun (kv : String × String) => if kv.1 = "arg" then Anderson2006b.Relation.ofString? kv.2 else none) r.paperFeatures

theorem Anderson2006b.rows_subject_selection (r : Data.Examples.LinguisticExample) : r ∈ Examples.all → r.id ≠ "andersonjm2006_4_8b" → subject (predicationOfRow r) = (r.feature? "subject").bind Relation.ofString?

Across the book's examples, the subject is the argument the hierarchy (38)′ selects — except (4.8b), whose complex absolutive outranks the simple one only under (38)'s optional comma.

As a linking theory

def Anderson2006b.andersonLinking : ArgumentStructure.Linking.LinkingTheory Predication Unit

Anderson's subject selection as a linking theory over predications: the subject's role is the label of the selected relation; the theory is silent on other functions.

Equations

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

theorem Anderson2006b.andersonLinking_subjects : andersonLinking.predict read () ArgumentStructure.Linking.GrammaticalFunction.subject = some ThetaRole.agent ∧ andersonLinking.predict fell () ArgumentStructure.Linking.GrammaticalFunction.subject = some ThetaRole.patient ∧ andersonLinking.predict knew () ArgumentStructure.Linking.GrammaticalFunction.subject = some ThetaRole.experiencer