Bobaljik (2000): The ins and outs of contextual allomorphy

Bobaljik argues that Vocabulary Insertion proceeds from the root outward and rewrites each morpheme as its exponent, so that an allomorph can look outward only at bare morphosyntactic features and inward only at diacritics and inserted vocabulary items. In Itelmen the Class II marker sees the root's class diacritic inward and both agreement nodes outward, while the subject prefix, inserted last, sees nothing of the object. In Chukchi the third-person subject prefix ne- is absent exactly when the object suffix is -nin or -ninet; since a third-singular object presents the same features whatever its subject, the trigger is the inserted item, an inward sensitivity.

Main statements

• Itelmen.rows_morphs, Chukchi.rows_morphs: the Itelmen verbs and the Chukchi Past I paradigm derive from one Vocabulary each.
• Itelmen.prefix_sees_no_object: when the subject prefix is inserted, nothing of the object agreement remains for it to be conditioned by; under non-deletion it would remain.
• Chukchi.object_features_cannot_bleed: a deletion of ne- keyed to the object's features overapplies under non-deletion and never applies under rewriting.
• Chukchi.ditransitive_retains_prefix: when the verb agrees with a second-person dative, a third-singular subject acting on a third-singular direct object keeps ne-.

Implementation notes

• Context is hierarchical. Mood is omitted, every form being realis or indicative, and the Chukchi Past I has no overt tense, so its T node is omitted.
• Every Itelmen verb has the class position, which the paper allows to be syntactic or added after syntax; in Class I it is null.
• Third-person objects carry person and number, as the paper's Chukchi trees and vocabulary write them, not the personless third person of its Itelmen agreement analysis.
• The rows list the paper's citation forms of the subject prefix t- and the present -s-, which two Itelmen examples print as t’ and z.

References

• J. D. Bobaljik, The ins and outs of contextual allomorphy
• M. Halle and A. Marantz, Distributed Morphology and the pieces of inflection

inductive Bobaljik2000.Feature : Type

A terminal carries present tense, the class position, the Class II diacritic, or an agreement node with person and number; an inserted vocabulary item is a morphophonological feature.

• pres : Feature
• classII : Feature
• classMarker : Feature
• agrO : Feature
• agrS : Feature
• first : Feature
• second : Feature
• third : Feature
• sg : Feature
• pl : Feature
• item (e : String) : Feature

def Bobaljik2000.instDecidableEqFeature.decEq (x✝ x✝¹ : Feature) : Decidable (x✝ = x✝¹)

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@[instance_reducible]

instance Bobaljik2000.instDecidableEqFeature : DecidableEq Feature

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• Bobaljik2000.instDecidableEqFeature = Bobaljik2000.instDecidableEqFeature.decEq

@[instance_reducible]

instance Bobaljik2000.instReprFeature : Repr Feature

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• Bobaljik2000.instReprFeature = { reprPrec := Bobaljik2000.instReprFeature.repr }

def Bobaljik2000.instReprFeature.repr : Feature → ℕ → Std.Format

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• Bobaljik2000.instReprFeature.repr Bobaljik2000.Feature.pres prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Bobaljik2000.Feature.pres")).group prec✝
• Bobaljik2000.instReprFeature.repr Bobaljik2000.Feature.agrO prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Bobaljik2000.Feature.agrO")).group prec✝
• Bobaljik2000.instReprFeature.repr Bobaljik2000.Feature.agrS prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Bobaljik2000.Feature.agrS")).group prec✝
• Bobaljik2000.instReprFeature.repr Bobaljik2000.Feature.sg prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Bobaljik2000.Feature.sg")).group prec✝
• Bobaljik2000.instReprFeature.repr Bobaljik2000.Feature.pl prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Bobaljik2000.Feature.pl")).group prec✝

def Bobaljik2000.itemFeatures (e : String) : List Feature

An inserted exponent presents its identity.

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• Bobaljik2000.itemFeatures e = [Bobaljik2000.Feature.item e]

def Bobaljik2000.morphs (dis : DistributedMorphology.ComplexHead.Discharge) (voc : List (DistributedMorphology.VocabularyItem Feature String)) (w : DistributedMorphology.ComplexHead (DistributedMorphology.Morpheme Feature String) (DistributedMorphology.Morpheme Feature String)) : List String

The surface exponents after inside-out insertion under hierarchical locality, null exponents dropped.

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def Bobaljik2000.stepContext (voc : List (DistributedMorphology.VocabularyItem Feature String)) (w : DistributedMorphology.ComplexHead (DistributedMorphology.Morpheme Feature String) (DistributedMorphology.Morpheme Feature String)) (dis : DistributedMorphology.ComplexHead.Discharge) (i : ℕ) : DistributedMorphology.Neighborhood (List Feature)

The context head i presents when inside-out insertion reaches it.

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def Bobaljik2000.phi : String → Option (List Feature)

The person and number of an argument, as the rows name them.

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• Bobaljik2000.phi "1sg" = some [Bobaljik2000.Feature.first, Bobaljik2000.Feature.sg]
• Bobaljik2000.phi "2sg" = some [Bobaljik2000.Feature.second, Bobaljik2000.Feature.sg]
• Bobaljik2000.phi "3sg" = some [Bobaljik2000.Feature.third, Bobaljik2000.Feature.sg]
• Bobaljik2000.phi "1pl" = some [Bobaljik2000.Feature.first, Bobaljik2000.Feature.pl]
• Bobaljik2000.phi "2pl" = some [Bobaljik2000.Feature.second, Bobaljik2000.Feature.pl]
• Bobaljik2000.phi "3pl" = some [Bobaljik2000.Feature.third, Bobaljik2000.Feature.pl]
• Bobaljik2000.phi x✝ = none

def Bobaljik2000.exponents (ex : Datum) : List String

A row's exponents, in linear order.

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• Bobaljik2000.exponents ex = List.filterMap ex.feature? ["m1", "m2", "m3", "m4", "m5"]

Itelmen

def Bobaljik2000.Itelmen.vocab : List (DistributedMorphology.VocabularyItem Feature String)

Present -s-. The Class II marker is conditioned inward by the root's class diacritic, past the tense suffix, and outward by both agreement nodes, -ki- marking a first-person subject acting on a third-person object and -čŋ- a second-singular subject; Class I is null. Third-person object agreement (8) is -čen, plural -čeʔn, under a first-person subject and -in, plural -iʔn, under a second-singular one. The subject prefix is t- for first singular and null for second singular.

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def Bobaljik2000.Itelmen.word (r : String) (cls subj obj : List Feature) : DistributedMorphology.ComplexHead (DistributedMorphology.Morpheme Feature String) (DistributedMorphology.Morpheme Feature String)

The verb is the root with its class diacritics, then present tense, the class position, and the object and subject agreement nodes, as in (16).

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def Bobaljik2000.Itelmen.rootClass : String → Option (List Feature)

The class diacritics of a root, as the rows name its class.

Equations

• Bobaljik2000.Itelmen.rootClass "I" = some []
• Bobaljik2000.Itelmen.rootClass "II" = some [Bobaljik2000.Feature.classII]
• Bobaljik2000.Itelmen.rootClass x✝ = none

def Bobaljik2000.Itelmen.ofRow (ex : Datum) : Option (DistributedMorphology.ComplexHead (DistributedMorphology.Morpheme Feature String) (DistributedMorphology.Morpheme Feature String))

The verb of an Itelmen row.

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theorem Bobaljik2000.Itelmen.rows_morphs (ex : Datum) : ex ∈ Examples.all → ex.language = "itel1242" → Option.map (morphs DistributedMorphology.ComplexHead.Discharge.rewriting vocab) (ofRow ex) = some (exponents ex)

In the forms (9) and (10) the Class II marker appears where insertion finds the class diacritic inward, in the shape the agreement outward selects.

def Bobaljik2000.Itelmen.bring : DistributedMorphology.ComplexHead (DistributedMorphology.Morpheme Feature String) (DistributedMorphology.Morpheme Feature String)

The verb of (9b), t-tɸ-s-ki-čeʔn, is 'bring' with a first-singular subject and a third-plural object.

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theorem Bobaljik2000.Itelmen.class_marker_context : stepContext vocab bring DistributedMorphology.ComplexHead.Discharge.rewriting 1 = { focus := [Feature.classMarker], leftCtx := [[Feature.item "s"], [Feature.classII, Feature.item "tɸ"]], rightCtx := [[Feature.agrO, Feature.third, Feature.pl], [Feature.agrS, Feature.first, Feature.sg]] }

In (9b) the Class II marker sees the root's diacritic inward, past the tense suffix already rewritten as -s-, and both agreement nodes outward, bare.

theorem Bobaljik2000.Itelmen.prefix_sees_no_object : (stepContext vocab bring DistributedMorphology.ComplexHead.Discharge.rewriting 3).leftCtx = [[Feature.item "čeʔn"], [Feature.item "ki"], [Feature.item "s"], [Feature.classII, Feature.item "tɸ"]] ∧ (stepContext vocab bring DistributedMorphology.ComplexHead.Discharge.nondeletion 3).leftCtx.head? = some [Feature.agrO, Feature.third, Feature.pl, Feature.item "čeʔn"]

When the subject prefix of (9b) is reached, every morpheme inside it has been rewritten as its exponent, and nothing of the object agreement remains for the prefix to be conditioned by. Under the non-deletion of [HM93] the object's features would remain.

Chukchi

def Bobaljik2000.Chukchi.objectVocab : List (DistributedMorphology.VocabularyItem Feature String)

The Past I object suffixes (20) are -nin and -ninet under a third-singular subject (24), otherwise -ɣʔen and -net for a third-person object, and the first- and second-person suffixes.

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def Bobaljik2000.Chukchi.vocab : List (DistributedMorphology.VocabularyItem Feature String)

The object suffixes, and the third-person subject prefix ne-, impoverished to zero inward of the item -nin or -ninet.

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def Bobaljik2000.Chukchi.word (r : String) (subj obj : List Feature) : DistributedMorphology.ComplexHead (DistributedMorphology.Morpheme Feature String) (DistributedMorphology.Morpheme Feature String)

The Past I verb is the root with the object and subject agreement nodes.

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def Bobaljik2000.Chukchi.agreesWith (dObj : List Feature) : Option (List Feature) → List Feature

Object agreement targets a first- or second-person indirect object over a third-person direct object, by the person hierarchy of §3.2.2, and otherwise the direct object.

Equations

• Bobaljik2000.Chukchi.agreesWith dObj (some io) = if Bobaljik2000.Feature.third ∈ dObj ∧ Bobaljik2000.Feature.third ∉ io then io else dObj
• Bobaljik2000.Chukchi.agreesWith dObj none = dObj

def Bobaljik2000.Chukchi.ofRow (ex : Datum) : Option (DistributedMorphology.ComplexHead (DistributedMorphology.Morpheme Feature String) (DistributedMorphology.Morpheme Feature String))

The verb of a Chukchi row.

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theorem Bobaljik2000.Chukchi.rows_morphs (ex : Datum) : ex ∈ Examples.all → ex.language = "chuk1273" → Option.map (morphs DistributedMorphology.ComplexHead.Discharge.rewriting vocab) (ofRow ex) = some (exponents ex)

Across the Past I paradigm (19) and the ditransitive (27), ne- is absent exactly where -nin or -ninet is inserted.

def Bobaljik2000.Chukchi.pseudoVocab : List (DistributedMorphology.VocabularyItem Feature String)

The impossible Pseudo-Chukchi rule (28a), deleting ne- in the context of a third-singular object rather than of the item -nin.

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theorem Bobaljik2000.Chukchi.object_features_cannot_bleed : morphs DistributedMorphology.ComplexHead.Discharge.nondeletion pseudoVocab (word "ɬʔu" [Feature.third, Feature.pl] [Feature.third, Feature.sg]) = ["ɬʔu", "ɣʔen"] ∧ morphs DistributedMorphology.ComplexHead.Discharge.rewriting pseudoVocab (word "ɬʔu" [Feature.third, Feature.sg] [Feature.third, Feature.sg]) = ["ne", "ɬʔu", "nin"]

A third-singular object presents the same features under a third-singular subject, where it is spelled out -nin, and under a third-plural one, where it is -ɣʔen (23). Keyed to those features, as in (28a), the deletion of ne- overapplies under non-deletion, removing the prefix of (19i). Under rewriting the features are gone when the prefix is inserted, so the deletion never applies, leaving the prefix of (19c).

theorem Bobaljik2000.Chukchi.ditransitive_retains_prefix : morphs DistributedMorphology.ComplexHead.Discharge.rewriting vocab (word "ɬʔu" [Feature.third, Feature.sg] (agreesWith [Feature.third, Feature.sg] none)) = ["ɬʔu", "nin"] ∧ morphs DistributedMorphology.ComplexHead.Discharge.rewriting vocab (word "jəl" [Feature.third, Feature.sg] (agreesWith [Feature.third, Feature.sg] (some [Feature.second, Feature.sg]))) = ["ne", "jəl", "ɣət"]

In both (19c) and (27) a third-singular subject acts on a third-singular direct object. In (27) the verb agrees with the second-person dative instead, -nin is not inserted, and ne- stays, so the prefix tracks the item, not the syntactic configuration.