Docs / Morphology / Paradigm / Contiguity

Paradigm contiguity: the *ABA generalization

import Linglib.Morphology.Paradigm.Contiguity · namespace Morphology

The *ABA generalization says graded paradigms are contiguous (IsContiguous), no form recurring across a distinct intervening form, for degree (positive < comparative < superlative, after Bobaljik), case (after Caha), and path roles (after Pantcheva). Of the five syncretism patterns of three cells, named as Bobaljik names the degree patterns, contiguity excludes exactly ABA.

Main definitions

Paradigm.aaa, Paradigm.abb, Paradigm.abc, Paradigm.aba, Paradigm.aab: the three-cell patterns.

Main results

isContiguous_iff_ker_ne_ker_aba: over three cells contiguity excludes exactly ABA.
ker_eq_ker_aba_iff, ker_eq_ker_aab_iff, ker_eq_ker_abc_iff, ker_eq_ker_iff_fin_three: the three-cell patterns by equalities of their cells.

References

Bobaljik 2012, Universals in comparative morphology: Suppletion, superlatives, and the structure of words formalized
Caha 2009, The Nanosyntax of Case formalized
Pantcheva 2011, Decomposing Path: The Nanosyntax of Directional Expressions formalized

The three-cell patterns

The five syncretism patterns of a three-cell chain, as form-class indices, named as Bobaljik 2012 names the degree patterns over positive < comparative < superlative. A concrete paradigm has a pattern when its syncretism, the kernel Setoid.ker, is the pattern's. ABA is the pattern contiguity excludes; AAB is contiguous, and its exclusion for degree is a vocabulary-level matter (Morphology/Exponence/Containment/Contiguity.lean).

The AAA pattern has one form throughout (tall – taller – tallest).

def Paradigm.aaa L52–53

:

Paradigm.aaa = ![0, 0, 0]

Used in Suppletion/Theory, Bobaljik2012, Dekier2021, SmithMoskalEtAl2019

In the ABB pattern the two upper cells share a form the lowest lacks (good – better – best).

def Paradigm.abb L55–57

:

Paradigm.abb = ![0, 1, 1]

Used in Suppletion/Theory, Bobaljik2012, Dekier2021, Graf2019, SmithMoskalEtAl2019

The ABC pattern has three forms (bonus – melior – optimus).

def Paradigm.abc L59–60

:

Paradigm.abc = ![0, 1, 2]

Used by ker_eq_ker_abc_iff

Used in Suppletion/Theory, Bobaljik2012, Dekier2021, Graf2019

In the ABA pattern the outer cells share a form the middle one lacks.

def Paradigm.aba L62–63

:

Paradigm.aba = ![0, 1, 0]

Used by ker_eq_ker_aba_iff, isContiguous_iff_ker_ne_ker_aba

Used in Suppletion/Bobaljik2012, Suppletion/SmithMoskalEtAl2019, Suppletion/Theory, Bobaljik2012, Graf2019

In the AAB pattern the two lower cells share a form the highest lacks.

def Paradigm.aab L65–66

:

Paradigm.aab = ![0, 0, 1]

Used by ker_eq_ker_aab_iff

Used in Suppletion/Bobaljik2012, Suppletion/SmithMoskalEtAl2019, Suppletion/Theory, Bobaljik2012, Dekier2021 and 2 more

A three-cell paradigm has the ABA pattern iff its outer cells agree and its middle cell differs.

theorem ker_eq_ker_aba_iff L83–99

{F : Type u_1} (p : Paradigm 3 F) :

Setoid.ker p = Setoid.ker Paradigm.aba ↔ p 0 = p 2 ∧ p 0 ≠ p 1

Built from

A three-cell paradigm has the AAB pattern iff its lower cells agree and its highest cell differs.

theorem ker_eq_ker_aab_iff L101–117

{F : Type u_1} (p : Paradigm 3 F) :

Setoid.ker p = Setoid.ker Paradigm.aab ↔ p 0 = p 1 ∧ p 1 ≠ p 2

Built from

A three-cell paradigm has the ABC pattern iff its cells differ pairwise.

theorem ker_eq_ker_abc_iff L119–134

{F : Type u_1} (p : Paradigm 3 F) :

Setoid.ker p = Setoid.ker Paradigm.abc ↔ p 0 ≠ p 1 ∧ p 1 ≠ p 2 ∧ p 0 ≠ p 2

Built from

Two three-cell paradigms have the same pattern iff the same pairs of cells agree.

theorem ker_eq_ker_iff_fin_three L136–150

{F : Type u_1} {G : Type u_2} (p : Paradigm 3 F) (q : Paradigm 3 G) :

Setoid.ker p = Setoid.ker q ↔ (p 0 = p 1 ↔ q 0 = q 1) ∧ (p 1 = p 2 ↔ q 1 = q 2) ∧ (p 0 = p 2 ↔ q 0 = q 2)

ABA is the only three-cell pattern contiguity excludes.

theorem isContiguous_iff_ker_ne_ker_aba L152–155

{F : Type u_1} (p : Paradigm 3 F) :

IsContiguous p ↔ Setoid.ker p ≠ Setoid.ker Paradigm.aba

Built from