Impoverishment (Distributed Morphology)

@cite{halle-marantz-1993} @cite{bonet-1991}

Impoverishment is a postsyntactic operation that deletes features from a terminal node before Vocabulary Insertion. It is the DM mechanism for deriving syncretism: when two morphosyntactic contexts share an exponent, this can be explained by one context losing a distinguishing feature, making it fall together with the other at VI.

Architecture

An Impoverishment rule specifies:

1. A trigger condition: which features/contexts license deletion
2. A target: which feature(s) are deleted

After Impoverishment applies, the terminal has fewer features, which may cause a less specific Vocabulary Item to be inserted (yielding syncretism or default morphology).

Connection to Mam

@cite{scott-2023} (ch. 4) analyzes pronoun reduction in SJA Mam as deletion of the pronominal base morpheme when its features are redundantly expressed by agreement. This is structurally parallel to Impoverishment: features on the pronoun node are deleted (at PF) when they are recoverable from agreement, yielding a reduced form.

structure Morphology.DM.Impoverishment.ImpoverishmentRule : Type

An Impoverishment rule: deletes features matching a condition from a feature bundle.

• condition: which features trigger Impoverishment (the structural context / feature environment)
• target: which feature to delete when the condition is met

• condition : Minimalism.FeatureBundle → Bool

  Does this rule apply in the given feature context?

• target : Minimalism.FeatureVal

  Which feature type is deleted?

def Morphology.DM.Impoverishment.deleteFeature (fb : Minimalism.FeatureBundle) (target : Minimalism.FeatureVal) : Minimalism.FeatureBundle

Delete all features matching target from a bundle.

Equations

• Morphology.DM.Impoverishment.deleteFeature fb target = List.filter (fun (f : Minimalism.GramFeature) => !f.featureType.sameType target) fb

def Morphology.DM.Impoverishment.applyImpoverishment (rule : ImpoverishmentRule) (fb : Minimalism.FeatureBundle) : Minimalism.FeatureBundle

Apply an Impoverishment rule: if the condition is met, delete the target feature; otherwise return the bundle unchanged.

Equations

• Morphology.DM.Impoverishment.applyImpoverishment rule fb = if rule.condition fb = true then Morphology.DM.Impoverishment.deleteFeature fb rule.target else fb

def Morphology.DM.Impoverishment.applyImpoverishmentChain (rules : List ImpoverishmentRule) (fb : Minimalism.FeatureBundle) : Minimalism.FeatureBundle

Apply a sequence of Impoverishment rules in order.

Equations

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

def Morphology.DM.Impoverishment.allRecoverable (recoverable pronFeatures : List Minimalism.FeatureVal) : Bool

A feature is redundant when it is recoverable from another source (e.g., agreement morphology on the verb). This is the mechanism underlying pronoun reduction in Mam (@cite{scott-2023}, ch. 4): when all features of the pronominal base are also expressed by agreement, the base is deleted at PF.

recoverable lists the features that are independently expressed (e.g., by agreement). pronFeatures lists the features on the pronoun. The pronoun base is deleted iff all its features are recoverable.

Equations

• Morphology.DM.Impoverishment.allRecoverable recoverable pronFeatures = pronFeatures.all fun (f : Minimalism.FeatureVal) => recoverable.any fun (x : Minimalism.FeatureVal) => f.sameType x

def Morphology.DM.Impoverishment.redundancyRule (source : List Minimalism.FeatureVal) (target : Minimalism.FeatureVal) : ImpoverishmentRule

Build a redundancy-based Impoverishment rule: delete target when the bundle contains features that are all recoverable from source.

Equations

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

theorem Morphology.DM.Impoverishment.deleteFeature_idempotent (fb : Minimalism.FeatureBundle) (target : Minimalism.FeatureVal) : deleteFeature (deleteFeature fb target) target = deleteFeature fb target

Deleting a feature then deleting it again is the same as deleting once. (Filter is idempotent when the predicate is stable.)