Docs / Morphology / Paradigm / Analogy

Proportional analogy

import Linglib.Morphology.Paradigm.Analogy · namespace Morphology

Source

A paradigm system p : ParadigmSystem L Cell F gives the form of each lexeme at each cell. It is analogical under a class of operations on forms when the forms at any two cells are related by one operation of the class, the same for every lexeme, as in walk : walks = jump : jumps. Under arbitrary operations this says only that the form at each cell determines the form at every other cell. Under the translations of an additive group it says that the shift between two cells is the same for every lexeme, which holds iff the family is a lexeme part plus a cell part.

Main definitions

Main statements

References

Declarations

Analogy under arbitrary operations says only that the form at each cell determines the form at every other cell.

theorem isAnalogical_univ_iffL54–61
{L : Type u_1} {Cell : Type u_2} {F : Type u_3} {p : ParadigmSystem L Cell F} :
IsAnalogical Set.univ p ↔ ∀ (c c' : Cell), Function.FactorsThrough (fun (x : L) => p x c') fun (x : L) => p x c

Built from

A paradigm system is analogically regular when it is analogical under translations, so that the shift from the form at one cell to the form at another is the same for every lexeme.

def IsAnalogicallyRegularL67–70
{L : Type u_1} {Cell : Type u_2} {F : Type u_3} [Add F] (p : ParadigmSystem L Cell F) :
Prop

Built from

Used by IsAnalogicallyRegular.map, isAnalogicallyRegular_iff, isAnalogicallyRegular_add, isAnalogicallyRegular_iff_exists_add

Used in Processing/DiscriminativeLexicon/Realization, HeitmeierChuangBaayen2026

L93–96