The discriminative lexicon as a realization

A linear DLM realises a lexeme at a paradigm cell as the form its production map predicts from the cell's meaning. Which meaning is the speaker's choice ([heitmeier-chuang-baayen-2026] Table 12.7): 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. Either way, on the shared Morphology.Realization interface this is a total, univalent realization, which puts the model beside Distributed Morphology, Paradigm Function Morphology and nanosyntax on the same paradigm data. The model itself posits no stems or exponents (Box 1.3); its lexeme and inflectional function are semantic primitives (ch. 5), and the interface is linglib's comparison device, not the theory's ontology. Over imputed semantics the form table is analogically regular by construction (Morphology.IsAnalogicallyRegular), which Studies/HeitmeierChuangBaayen2026 turns into an iff; over word-specific embeddings it need not be.

Main declarations

• DiscriminativeLexicon.Linear.paradigm D s — the model's form table over a meaning assignment s to lexemes at cells.
• DiscriminativeLexicon.Linear.realization D s — the same as a Morphology.Realization, total and univalent.
• DiscriminativeLexicon.Linear.isAnalogicallyRegular_paradigm_imputed — over imputed semantics the table is analogically regular.

References

• [M. Heitmeier, Y.-Y. Chuang and R. H. Baayen, The Discriminative Lexicon (2026)][heitmeier-chuang-baayen-2026]

def DiscriminativeLexicon.Linear.paradigm {n d : ℕ} {L : Type u_1} {Cell : Type u_2} (D : Linear ℝ (FormVec n) (MeaningVec d)) (s : L → Cell → MeaningVec d) (l : L) (c : Cell) : FormVec n

The form table of a linear DLM over a meaning assignment: the production map at the meaning of each lexeme at each cell.

Equations

• D.paradigm s l c = D.production (s l c)

@[simp]

theorem DiscriminativeLexicon.Linear.paradigm_apply {n d : ℕ} {L : Type u_1} {Cell : Type u_2} (D : Linear ℝ (FormVec n) (MeaningVec d)) (s : L → Cell → MeaningVec d) (l : L) (c : Cell) : D.paradigm s l c = D.production (s l c)

def DiscriminativeLexicon.Linear.realization {n d : ℕ} {L : Type u_1} {Cell : Type u_2} (D : Linear ℝ (FormVec n) (MeaningVec d)) (s : L → Cell → MeaningVec d) : Morphology.Realization L Cell (FormVec n)

A linear DLM as a Morphology.Realization: a lexeme at a cell is realised by the one form the production map predicts.

Equations

• D.realization s = { realize := fun (l : L) (c : Cell) => {D.paradigm s l c} }

@[simp]

theorem DiscriminativeLexicon.Linear.realization_realize {n d : ℕ} {L : Type u_1} {Cell : Type u_2} (D : Linear ℝ (FormVec n) (MeaningVec d)) (s : L → Cell → MeaningVec d) (l : L) (c : Cell) : (D.realization s).realize l c = {D.paradigm s l c}

theorem DiscriminativeLexicon.Linear.realization_isTotal {n d : ℕ} {L : Type u_1} {Cell : Type u_2} (D : Linear ℝ (FormVec n) (MeaningVec d)) (s : L → Cell → MeaningVec d) : (D.realization s).IsTotal

theorem DiscriminativeLexicon.Linear.realization_isUnivalent {n d : ℕ} {L : Type u_1} {Cell : Type u_2} (D : Linear ℝ (FormVec n) (MeaningVec d)) (s : L → Cell → MeaningVec d) : (D.realization s).IsUnivalent

theorem DiscriminativeLexicon.Linear.isAnalogicallyRegular_paradigm_imputed {n d : ℕ} {L : Type u_1} {Cell : Type u_2} (D : Linear ℝ (FormVec n) (MeaningVec d)) (σ : L → MeaningVec d) (ε : Cell → MeaningVec d) : Morphology.IsAnalogicallyRegular (D.paradigm (imputed σ ε))

Over imputed semantics the form table is analogically regular: the form shift of a cell is lexeme-independent.