Alexiadou and Lohndal (2017): The structural configurations of root categorization

Distributed Morphology agrees that a Root is categorized by a functional head, but not on the configuration. The Root may be merged as the complement of the categorizer, as its modifier, as either according to its class, or inserted after syntax into a position of its own. The chapter weighs the evidence for each view and finds none conclusive. Hiaki suppletion, offered for Roots that take their internal argument as a complement, survives on a derivation in which the Root never takes one: the Root moves into a low head, and the argument merges with the complex head they form, local enough under the refined locality condition. One-replacement and the selection of objects across categories fail to decide too: a noun with arguments is derived from a verb, its nP embedding the verbal structure, so whatever the configuration of the Root and its argument, one strands adjuncts and not arguments and the noun's argument is selected as the verb's. Without a secondary resultative predicate, Direct Merge of a Root and its merger as a complement are practically indistinguishable. What does favor letting Roots merge in either way is a contrast in resultatives: colored dark is possible and blackened dark is not, since only a Root that can modify v leaves v's complement free for an aP. Inserting Roots after syntax into the empty position that Primary Merge leaves derives that the material over a Root labels it, but not that a Root is categorized at all.

Main statements

• mayCondition'_tree27: in the derivation of (27) the internal argument may condition the Root under the refined locality condition, though the Root takes no complement, while in the representation (26) it may not.
• deverbal_derives: in a deverbal noun every configuration of the Root and its argument derives the one-replacement contrast of (8) and selects the argument as the verb does.
• root_without_categorizer: when Roots are inserted after syntax, a derivation builds a Root from a resource with no categorizer.
• derives_iff: of the four views only the one that merges some Roots as modifiers and others as complements derives the contrast of (56).

Implementation notes

• The locality condition (25) is the one the chapter quotes from the manuscript of Bobaljik and Harley's chapter, DistributedMorphology.MayCondition', and the trees are over the categories of BobaljikHarley2017. In (27c) the lower F is the complex head of F and the Root.
• That Direct Merge and complement Merge build one complex head is Embick2004.headDaughter?_moveRoot.
• A view's licensing of a resultative aP is read off how it attaches a Root of each class: a v with a Root as its complement has no room for an aP, as Embick's analysis of v[FIENT] requires (interpretable_aP_iff).
• one stands for the nP over the verbal structure, with the adjunct adjoined to it; the chapter places both at ClP, which is above the verbal structure too.

TODO

The discussion of verb–object idioms, the generalization that only nouns derived from verbs have argument structure, and the endocentricity argument for Roots as modifiers are not formalized.

References

• [AL17]
• [BH17]
• [Emb04]

Hiaki suppletion without Root complements

def AlexiadouLohndal2017.tree26 : BobaljikHarley2017.T

The structure (26), the internal argument in the specifier of F over vP, the Root in situ.

Equations

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

def AlexiadouLohndal2017.tree27 : BobaljikHarley2017.T

The last step of the derivation (27). Once vP is spelled out, the Root forms a complex head with F, and the internal argument merges with that head.

Equations

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theorem AlexiadouLohndal2017.mayCondition'_tree27 : DistributedMorphology.MayCondition' tree27 { toList := [1, 1] } { toList := [0] } ∧ ¬DistributedMorphology.MayCondition tree26 { toList := [1, 1, 1, 1, 1] } { toList := [1, 1, 0] }

Suppletion without a Root complement. In (27) the internal argument may condition the Root under (25), since only the complex head lies between them, while in the representation (26) the vP and the projection of F intervene, under either formulation of locality.

The four views and the resultative contrast

inductive AlexiadouLohndal2017.View : Type

The four views of how a Root is categorized (6) merge it as the complement of v, as its modifier, or as either according to its class, or insert it after syntax.

• complement : View
• modifier : View
• mixed : View
• postSyntactic : View

@[instance_reducible]

instance AlexiadouLohndal2017.instDecidableEqView : DecidableEq View

Equations

• AlexiadouLohndal2017.instDecidableEqView x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance AlexiadouLohndal2017.instReprView : Repr View

Equations

• AlexiadouLohndal2017.instReprView = { reprPrec := AlexiadouLohndal2017.instReprView.repr }

def AlexiadouLohndal2017.instReprView.repr : View → ℕ → Std.Format

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

inductive AlexiadouLohndal2017.RootClass : Type

The classes of Roots, manner Roots like √COLOR and state or result Roots like √BLACK.

• manner : RootClass
• result : RootClass

@[instance_reducible]

instance AlexiadouLohndal2017.instDecidableEqRootClass : DecidableEq RootClass

Equations

• AlexiadouLohndal2017.instDecidableEqRootClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance AlexiadouLohndal2017.instReprRootClass : Repr RootClass

Equations

• AlexiadouLohndal2017.instReprRootClass = { reprPrec := AlexiadouLohndal2017.instReprRootClass.repr }

def AlexiadouLohndal2017.instReprRootClass.repr : RootClass → ℕ → Std.Format

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inductive AlexiadouLohndal2017.Attachment : Type

A Root is attached to v as its complement or as its modifier.

• complement : Attachment
• modifier : Attachment

@[instance_reducible]

instance AlexiadouLohndal2017.instDecidableEqAttachment : DecidableEq Attachment

Equations

• AlexiadouLohndal2017.instDecidableEqAttachment x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def AlexiadouLohndal2017.instReprAttachment.repr : Attachment → ℕ → Std.Format

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

@[instance_reducible]

instance AlexiadouLohndal2017.instReprAttachment : Repr Attachment

Equations

• AlexiadouLohndal2017.instReprAttachment = { reprPrec := AlexiadouLohndal2017.instReprAttachment.repr }

def AlexiadouLohndal2017.View.attach : View → RootClass → Option Attachment

How each view attaches a Root of each class to v; a Root inserted after syntax is attached in neither way.

Equations

• AlexiadouLohndal2017.View.complement.attach x✝ = some AlexiadouLohndal2017.Attachment.complement
• AlexiadouLohndal2017.View.modifier.attach x✝ = some AlexiadouLohndal2017.Attachment.modifier
• AlexiadouLohndal2017.View.mixed.attach AlexiadouLohndal2017.RootClass.manner = some AlexiadouLohndal2017.Attachment.modifier
• AlexiadouLohndal2017.View.mixed.attach AlexiadouLohndal2017.RootClass.result = some AlexiadouLohndal2017.Attachment.complement
• AlexiadouLohndal2017.View.postSyntactic.attach x✝ = none

def AlexiadouLohndal2017.View.LicensesResultative (v : View) (c : RootClass) : Prop

A view licenses a Root of a class with a resultative aP when it attaches the Root as v's modifier, since a Root that is v's complement leaves no room for an aP.

Equations

• v.LicensesResultative c = (v.attach c = some AlexiadouLohndal2017.Attachment.modifier)

@[instance_reducible]

instance AlexiadouLohndal2017.instDecidableLicensesResultative (v : View) (c : RootClass) : Decidable (v.LicensesResultative c)

Equations

• AlexiadouLohndal2017.instDecidableLicensesResultative v c = AlexiadouLohndal2017.instDecidableLicensesResultative._aux_1 v c

theorem AlexiadouLohndal2017.interpretable_aP_iff (x : Embick2004.DP) (m : Option Embick2004.Root) (a : Embick2004.Root) (μ : Embick2004.MeansRule) : { spec := some x, merged := m, comp := Embick2004.Complement.aP a, means := some μ }.Interpretable ↔ m.isSome = true

In Embick's analysis of v[FIENT] an aP complement has an interpretation exactly when a Root is directly merged with v[FIENT].

def AlexiadouLohndal2017.classTable : List (String × RootClass)

The classes as named in the rows.

Equations

• AlexiadouLohndal2017.classTable = [("manner", AlexiadouLohndal2017.RootClass.manner), ("result", AlexiadouLohndal2017.RootClass.result)]

def AlexiadouLohndal2017.data : List (RootClass × Judgment)

The resultative examples, the class of their Root with their judgment.

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theorem AlexiadouLohndal2017.data_length : data.length = 2

theorem AlexiadouLohndal2017.derives_iff (v : View) : (∀ p ∈ data, p.2 = Judgment.acceptable ↔ v.LicensesResultative p.1) ↔ v = View.mixed

Only the mixed view derives (56). A view derives the contrast when the resultative of each example is acceptable exactly where the view licenses it. The views that attach every Root in the same way give colored dark and blackened dark the same status, and only the view that merges manner Roots as modifiers and result Roots as complements tells them apart.

One-replacement and selection in deverbal nouns

def AlexiadouLohndal2017.deverbal (c : VanCraenenbroeck2014.Config) : PhraseStructure.Tree DistributedMorphology.RootCategorization.Cat Unit

A deverbal noun with an adjunct, the nP of a nominalizer over the phrase of a Root and its argument under v, with a PP adjoined to it.

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

def AlexiadouLohndal2017.position (c : VanCraenenbroeck2014.Config) : Harley2014.Dependent → Core.Order.TreePath

The position of a dependent in deverbal.

Equations

• AlexiadouLohndal2017.position c Harley2014.Dependent.argument = { toList := 0 :: 1 :: c.argPos.toList }
• AlexiadouLohndal2017.position c Harley2014.Dependent.adjunct = { toList := [1] }

def AlexiadouLohndal2017.OneStrands (c : VanCraenenbroeck2014.Config) (d : Harley2014.Dependent) : Prop

one, a proform of the category of the noun, strands the dependent from the Root.

Equations

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

@[instance_reducible]

instance AlexiadouLohndal2017.instDecidableOneStrands (c : VanCraenenbroeck2014.Config) (d : Harley2014.Dependent) : Decidable (OneStrands c d)

Equations

• AlexiadouLohndal2017.instDecidableOneStrands c d = AlexiadouLohndal2017.instDecidableOneStrands._aux_1 c d

def AlexiadouLohndal2017.oneData : List (Harley2014.Dependent × Judgment)

The examples of (8), the dependent each strands with its judgment.

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theorem AlexiadouLohndal2017.oneData_length : oneData.length = 2

theorem AlexiadouLohndal2017.deverbal_derives (c : VanCraenenbroeck2014.Config) : (∀ p ∈ oneData, p.2 = Judgment.acceptable ↔ OneStrands c p.1) ∧ DistributedMorphology.RootCategorization.selector (deverbal c) (position c Harley2014.Dependent.argument) = DistributedMorphology.RootCategorization.selector (VanCraenenbroeck2014.Config.tree DistributedMorphology.Categorizer.v c) c.argPos

One-replacement and selection cannot decide. In a deverbal noun, whatever the configuration of the Root and its argument, one strands exactly the dependents (8) accepts stranded, and the argument is merged with the head the verb merges it with, unlike in a noun that categorizes the Root itself (Harley2014.selector_eq_iff).

Roots inserted after syntax

theorem AlexiadouLohndal2017.root_without_categorizer : ∃ (o : DeBelderVanCraenenbroeck2015.Obj DeBelderVanCraenenbroeck2015.Feature), Relation.ReflTransGen DeBelderVanCraenenbroeck2015.Step (DeBelderVanCraenenbroeck2015.State.init [{DeBelderVanCraenenbroeck2015.Feature.definite}, {DeBelderVanCraenenbroeck2015.Feature.plural}]) { resource := [], object := o } ∧ o.roots = 1 ∧ o.label = some {DeBelderVanCraenenbroeck2015.Feature.definite}

A Root need not be categorized. Primary Merge pairs the null derivation with whichever item it selects first, and that item labels the result, so the derivation of the books builds a Root from its definite and plural features alone, labelled by the definite feature.