Docs / Processing / DiscriminativeLexicon / Realization

The discriminative lexicon as a realization

import Linglib.Processing.DiscriminativeLexicon.Realization · namespace DiscriminativeLexicon

This file presents the form table of a production matrix as a Morphology.ParadigmSystem, and so as a total, univalent Morphology.Realization (ParadigmSystem.toRealization), so that the discriminative lexicon stands beside Distributed Morphology, Paradigm Function Morphology and nanosyntax on the same paradigm data.

A production matrix realizes a lexeme at a paradigm cell as the form it predicts from the cell's meaning. Which meaning is used is the speaker's choice in Table 12.7 of Heitmeier, Chuang and Baayen, either an empirical embedding of the word or a meaning constructed from the lexeme's vector and the inflectional function's vector (imputed), the meaning of walked as the meaning of walk plus a past-tense vector. The model itself posits no stems or exponents; its lexeme and inflectional function are semantic primitives, and the realization interface is linglib's comparison device rather than the theory's ontology. Imputed meanings are analogically regular (Morphology.IsAnalogicallyRegular), the shift from walk to walks being the shift from jump to jumps, and a production matrix carries regular meanings to regular forms, so over imputed semantics the form table is regular, which Studies/HeitmeierChuangBaayen2026 turns into an equivalence; over word-specific embeddings it need not be.

Main definitions

paradigm G s: the form table of a production matrix G over a meaning assignment s.

Main results

isAnalogicallyRegular_imputed: imputed meanings are analogically regular.
isAnalogicallyRegular_paradigm: a production matrix preserves analogical regularity.

References

M. Heitmeier, Y.-Y. Chuang and R. H. Baayen, The Discriminative Lexicon (2026)

Declarations

The form table of a production matrix over a meaning assignment lists the predicted form at the meaning of each lexeme at each cell.

def paradigm L50–52

{κ : Type u_1} {δ : Type u_2} {L : Type u_3} {Cell : Type u_4} [Fintype δ] (G : Matrix δ κ ℝ) (s : Morphology.ParadigmSystem L Cell (δ → ℝ)) :

Morphology.ParadigmSystem L Cell (κ → ℝ)

paradigm G s l c = Matrix.vecMul (s l c) G

Used by paradigm_apply, isAnalogicallyRegular_paradigm

Used in HeitmeierChuangBaayen2026

L54

Imputed meanings are analogically regular: the shift between two cells is the difference of their vectors for every lexeme (eqs. 1.10–1.12).

theorem isAnalogicallyRegular_imputed L56–61

{L : Type u_3} {Cell : Type u_4} {V : Type u_5} [AddCommGroup V] (σ : L → V) (ε : Cell → V) :

Morphology.IsAnalogicallyRegular (imputed σ ε)

A production matrix carries analogically regular meanings to analogically regular forms.

theorem isAnalogicallyRegular_paradigm L63–66

{κ : Type u_1} {δ : Type u_2} {L : Type u_3} {Cell : Type u_4} [Fintype δ] (G : Matrix δ κ ℝ) {s : Morphology.ParadigmSystem L Cell (δ → ℝ)} (h : Morphology.IsAnalogicallyRegular s) :

Morphology.IsAnalogicallyRegular (paradigm G s)

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