Morphomes: syncretism classes with no natural characterization

import Linglib.Morphology.Paradigm.Morphome · namespace Morphology

A realization map p : Cell → F assigns a form to each paradigm cell. Its syncretism relation — cells receiving the same form — is the kernel setoid Setoid.ker p, and the syncretism classes are its equivalence classes. A morphome (Aronoff 1994 coined the term) is a systematic syncretism that does not define a natural class; Herce 2023 adopts the working definition "a systematic morphological syncretism which does not define a (syntactically or semantically) natural class" (Trommer 2016, quoted approvingly).

Naturalness is a parameter Natural : Set Cell → Prop, not stipulated here. Herce 2023 operationalizes a natural class as one "coextensive with a value (e.g. SG) or conjunction of values (e.g. 1SG)" and treats naturalness as gradient, so Natural is best read as a threshold slice of that scale; the value-or-conjunction predicate is its canonical instantiation, IsValueConjunction: the cells agreeing with some cell on some of the paradigm's features, each feature given as the partition of cells it induces. Systematicity — recurrence of the pattern under more than one exponent or allomorph — is a separate criterion the consumer establishes.

Two limitations, per Baerman 2015's three-way analysis space for syncretism (morphosyntactic identity / underspecification / morphological stipulation, p. 146): an elsewhere form's fiber is typically also nontrivial and non-natural (one specified cell, the default covers the unnatural rest — Skou, p. 145), so IsMorphome is necessary but not sufficient for stipulation-hood; distinguishing the two needs opposition structure or the systematicity criterion above. And directional syncretism (a cell wearing another cell's form "in place of the expected" one, p. 142) is invisible to the symmetric kernel.

The vocabulary here is deliberately just "morphome": Herce 2023 rejects Round's rhizomorphome ~~metamorphome~~ meromorphome subdivision as needless jargon, and "metasyncretism" does not appear in the book.

Main declarations

Morphology.syncretismClass — the class (fiber) of a given cell
Morphology.formCells — the cells a form realizes, the Finset face of the class
Morphology.formCellsOf — the cells a table with defective or overabundant cells gives a form
Morphology.IsMorphome — a nontrivial syncretism class failing Natural
Morphology.IsValueConjunction — the cells agreeing with a witness on a set of features, Herce 2023's natural class

Declarations

The syncretism class of a cell a: every cell realized as a is.

def syncretismClass L60–61

{Cell : Type u_1} {F : Type u_2} (p : Cell → F) (a : Cell) :

Set Cell

syncretismClass p a = {x : Cell | p x = p a}

Used by syncretismClass_mem_classes, coe_formCells, isMorphome_syncretismClass

L63–65

The cells p realizes as the form f: the syncretism class of any cell realized as f, as a Finset.

def formCells L67–70

{Cell : Type u_1} {F : Type u_2} [Fintype Cell] [DecidableEq F] (p : Cell → F) (f : F) :

Finset Cell

formCells p f = {x : Cell | p x = f}

Used by mem_formCells, coe_formCells, isMorphome_of_formCells

Used in DalrympleKaplan2000, Herce2023, JackendoffAudring2020

L72–74

The cells a table p gives the form f, where a cell may have no form or several: the Finset face of a defective or overabundant paradigm, and of a segmented realization at one of its exponents.

def formCellsOf L76–80

{Cell : Type u_1} {F : Type u_2} [Fintype Cell] [DecidableEq F] (p : Cell → Finset F) (f : F) :

Finset Cell

formCellsOf p f = {x : Cell | f ∈ p x}

Used by mem_formCellsOf

Used in Fragments/Romance/Italian/Pronouns, Syntax/Category/Pronoun/Basic, Syntax/Category/Pronoun/Personal, Allotey2021, DalrympleKaplan2000

L82–84

L86–88

A morphome (Herce 2023): a syncretism class of p that groups more than one cell (Set.Nontrivial) yet is not a Natural class — a grouping visible only in the realization, with no phonological, syntactic, or semantic characterization (Aronoff 1994's "morphology by itself"). Natural is a parameter (see the module docstring).

def IsMorphome L90–96

{Cell : Type u_1} {F : Type u_2} (p : Cell → F) (Natural : Set Cell → Prop) (c : Set Cell) :

Prop

IsMorphome p Natural c = (c ∈ (Setoid.ker p).classes ∧ c.Nontrivial ∧ ¬Natural c)

Used by isMorphome_syncretismClass, isMorphome_of_formCells

Used in Herce2023, JackendoffAudring2020

L98–102

L104–110

Natural classes as value conjunctions

Herce 2023 takes a natural class to be one "coextensive with a value or conjunction of values". A paradigm's features are the partitions of its cells they induce, the kernels of the feature projections; a value conjunction is then the set of cells agreeing with some cell on some of the features.

A set of cells is a value conjunction for the features feats when it consists of the cells agreeing with some cell on some of the features.

def IsValueConjunction L121–124

{Cell : Type u_1} {ι : Type u_3} (feats : ι → Setoid Cell) (X : Set Cell) :

Prop

IsValueConjunction feats X = ∃ (S : Finset ι) (c₀ : Cell), X = {c : Cell | ∀ i ∈ S, (feats i) c c₀}

Used by isValueConjunction_coe_iff

Used in Herce2023, JackendoffAudring2020

L126–131