ten Wolde (2023): The English Binominal Noun Phrase

[tW23]

End-to-end study file connecting the core taxonomy, semantic theory, and English fragment data to the empirical claims in [tW23].

Key claims formalized

1. Six-way taxonomy (Table 2.2): N+PP, head-classifier, pseudo-partitive, evaluative BNP, evaluative modifier, binominal intensifier — each with distinct diagnostic profiles.

2. Grammaticalization cline (Ch. 5–6): N₁ nouns progress through the six stages with increasing semantic bleaching, loss of nounhood features (plural, number agreement), and reanalysis of [N₁ of a] as a constituent.

3. Three-way evaluative distinction (Table 4.2, Ch. 4): EBNP, EM, and BI are separate constructions with different semantic composition, premodification patterns, and diagnostic properties.

4. Semantic class predicts path (Ch. 5): inanimate N₁ nouns develop pseudo-partitive readings; animate and abstract N₁ nouns generally skip pseudo-partitive and enter evaluative uses directly.

Table 4.2: Overview of evaluative categories

The three evaluative constructions differ on multiple diagnostics. These theorems verify the Table 4.2 claims against the formalized diagnostic functions in Quantification.Binominal.

theorem TenWolde2023.ebnp_profile : Quantification.Binominal.OfBinominalType.evaluative.n₁AllowsPlural = true ∧ Quantification.Binominal.OfBinominalType.evaluative.det₂MarksNumber = true ∧ Quantification.Binominal.OfBinominalType.evaluative.ofReplaceableByCopula = true ∧ Quantification.Binominal.OfBinominalType.evaluative.n₁OfAIsConstituent = false

EBNP: N₁ allows plural, Det₂ marks number, of replaceable by copula.

theorem TenWolde2023.em_profile : Quantification.Binominal.OfBinominalType.evaluativeModifier.n₁AllowsPlural = false ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.det₂MarksNumber = false ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.ofReplaceableByCopula = false ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.n₁OfAIsConstituent = true

EM: N₁ frozen singular, Det₂ no longer marks number, [N₁ of a] is a constituent, of not replaceable by copula.

theorem TenWolde2023.bi_profile : Quantification.Binominal.OfBinominalType.binominalIntensifier.n₁AllowsPlural = false ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.det₂MarksNumber = false ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.ofReplaceableByCopula = false ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.n₁OfAIsConstituent = true

BI: same as EM on these diagnostics — further bleaching is syntactic (shifts into AdjP), not visible in these features.

theorem TenWolde2023.all_evaluative_n₂_headed : Quantification.Binominal.OfBinominalType.evaluative.head = Quantification.Binominal.BNPHead.n₂ ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.head = Quantification.Binominal.BNPHead.n₂ ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.head = Quantification.Binominal.BNPHead.n₂

All three evaluative types are N₂-headed.

theorem TenWolde2023.premod_distinguishes_evaluative_types : Quantification.Binominal.OfBinominalType.evaluative.n₁AllowsDescriptivePremod = true ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.n₁AllowsDescriptivePremod = false ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.n₁AllowsDescriptivePremod = false

Ch. 7, Table 4.2: N₁ premodification distinguishes EBNP from EM/BI. EBNP allows descriptive premodification of N₁ (a total idiot of a doctor); EM and BI block it (#a total hell of a time) because [N₁ of a] has been reanalyzed as a modifier unit.

theorem TenWolde2023.n₂_type_distinguishes_bi : Quantification.Binominal.OfBinominalType.evaluative.n₂AllowsMass = false ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.n₂AllowsMass = false ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.n₂AllowsMass = true

Table 4.2: N₂ type restriction distinguishes BI from EBNP/EM. EBNP and EM restrict N₂ to count/collective nouns; BI extends to mass.

theorem TenWolde2023.agreement_loosens_on_evaluative_path : Quantification.Binominal.OfBinominalType.evaluative.n₁N₂Agreement = Quantification.Binominal.AgreementLevel.agree ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.n₁N₂Agreement = Quantification.Binominal.AgreementLevel.usuallyAgree ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.n₁N₂Agreement = Quantification.Binominal.AgreementLevel.noAgreement

Table 4.2: N₁ & N₂ agreement loosens along the evaluative path.

theorem TenWolde2023.of_optional_at_bi : Quantification.Binominal.OfBinominalType.evaluative.ofObligatory = true ∧ Quantification.Binominal.OfBinominalType.evaluativeModifier.ofObligatory = true ∧ Quantification.Binominal.OfBinominalType.binominalIntensifier.ofObligatory = false

Table 4.2: of becomes optional at the BI stage.

Ch. 5–6: Diachronic path depends on N₁ semantic class

Inanimate nouns (cake, nub, breeze, husk) develop pseudo-partitive readings. Animate (beast, whale, snake) and abstract (hell, bitch) nouns generally skip pseudo-partitive.

theorem TenWolde2023.inanimate_develop_pseudopartitive : List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.cake.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.nub.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.breeze.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.husk.constructions = true

All inanimate entries have pseudo-partitive in their construction list.

theorem TenWolde2023.animate_skip_pseudopartitive : List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.beast.constructions = false ∧ List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.whale.constructions = false

Most animate entries skip pseudo-partitive (beast, whale).

theorem TenWolde2023.snake_exception : English.Binominals.snake.semanticClass = English.Binominals.N₁SemanticClass.animate ∧ List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.snake.constructions = true

Snake is the exception: an animate noun with pseudo-partitive.

theorem TenWolde2023.inanimate_class_predicts : English.Binominals.cake.semanticClass.developsPseudoPartitive = true ∧ English.Binominals.nub.semanticClass.developsPseudoPartitive = true ∧ English.Binominals.breeze.semanticClass.developsPseudoPartitive = true ∧ English.Binominals.husk.semanticClass.developsPseudoPartitive = true

The semantic class predicate agrees with the entry data for all inanimate nouns in the corpus.

The main grammaticalization path

[tW23] Ch. 8: the main evaluative path is N+PP → Head-Classifier → EBNP → EM → BI, skipping pseudo-partitive. Animate and abstract nouns follow this path; inanimate nouns may develop pseudo-partitive as an intermediate stage.

theorem TenWolde2023.animate_main_path : List.elem Quantification.Binominal.OfBinominalType.nPP English.Binominals.beast.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.headClassifier English.Binominals.beast.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.beast.constructions = false ∧ List.elem Quantification.Binominal.OfBinominalType.evaluative English.Binominals.beast.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.evaluativeModifier English.Binominals.beast.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.binominalIntensifier English.Binominals.beast.constructions = true

Animate nouns skip pseudo-partitive: beast and whale have evaluative uses but no pseudo-partitive attestations.

theorem TenWolde2023.abstract_main_path : List.elem Quantification.Binominal.OfBinominalType.nPP English.Binominals.bitch.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.pseudoPartitive English.Binominals.bitch.constructions = false ∧ List.elem Quantification.Binominal.OfBinominalType.evaluative English.Binominals.bitch.constructions = true ∧ List.elem Quantification.Binominal.OfBinominalType.evaluativeModifier English.Binominals.bitch.constructions = true

Abstract nouns also skip pseudo-partitive (except hell which participates in all six). bitch follows the main path.

theorem TenWolde2023.semantic_class_predicts_path : English.Binominals.beast.semanticClass.developsPseudoPartitive = false ∧ English.Binominals.whale.semanticClass.developsPseudoPartitive = false ∧ English.Binominals.bitch.semanticClass.developsPseudoPartitive = false ∧ English.Binominals.cake.semanticClass.developsPseudoPartitive = true ∧ English.Binominals.nub.semanticClass.developsPseudoPartitive = true

The semantic class predicate correctly predicts which nouns skip pseudo-partitive: animate and abstract predict no PP, inanimate predicts PP.

Ch. 5: hell is the most grammaticalized N₁ noun

hell participates in all six constructions and has developed reduced forms (helluva, hella), indicating advanced grammaticalization. whale also has a reduced form (whaleuva) but participates in only five constructions.

theorem TenWolde2023.hell_maximally_grammaticalized : English.Binominals.hell.constructions.length = 6 ∧ English.Binominals.hell.hasReducedForm = true

hell is the only N₁ in the dataset that participates in all six types.

theorem TenWolde2023.whale_reduced_not_all_six : English.Binominals.whale.hasReducedForm = true ∧ English.Binominals.whale.constructions.length = 5

whale has a reduced form (whaleuva) but only five constructions.

theorem TenWolde2023.hell_uniquely_all_six (e : English.Binominals.BinominalN₁Entry) : e ∈ English.Binominals.allN₁Entries → e.constructions.length = 6 → e.form = "hell"

hell is the only entry in the dataset with all six constructions.

Semantic composition across the three evaluative stages

Demonstrates the progression from EBNP (full gradable predicate) to EM (evaluative measure) to BI (degree intensifier) using the worked examples from Semantics/Lexical/Noun/Binominal.

theorem TenWolde2023.entailment_summary : (Quantification.Binominal.biSemantics (Semantics.Gradability.Intensification.muHorrible 10) Quantification.Binominal.doctorQuality (Degree.thr 5 ⋯) (Degree.thr 3 ⋯) (fun (b : Semantics.Gradability.GradableNouns.Person) => decide (Quantification.Binominal.isDoctor b)) Semantics.Gradability.GradableNouns.Person.george = true → Quantification.Binominal.emSemantics (Semantics.Gradability.Intensification.muHorrible 10) Quantification.Binominal.doctorQuality (Degree.thr 3 ⋯) (fun (b : Semantics.Gradability.GradableNouns.Person) => decide (Quantification.Binominal.isDoctor b)) Semantics.Gradability.GradableNouns.Person.george = true) ∧ Quantification.Binominal.ebnpSemantics Semantics.Gradability.GradableNouns.exampleIdiot (fun (b : Semantics.Gradability.GradableNouns.Person) => decide (Quantification.Binominal.isDoctor b)) Semantics.Gradability.GradableNouns.Person.sarah = true ∧ Quantification.Binominal.emSemantics (Semantics.Gradability.Intensification.muHorrible 10) Quantification.Binominal.doctorQuality (Degree.thr 3 ⋯) (fun (b : Semantics.Gradability.GradableNouns.Person) => decide (Quantification.Binominal.isDoctor b)) Semantics.Gradability.GradableNouns.Person.sarah = false

The three evaluative semantics form an entailment chain: BI → EM (proved), but EBNP is independent of EM.

The EBNP → EM → BI cline as subjectification

[tW23] §4.5: the EBNP → EM → BI transitions are driven by subjectification ([Tra10a]) — N₁ shifts from ascribing objective/physical properties to expressing the speaker's subjective evaluation. Steps use Traugott2010.SubjectificationStep.

def TenWolde2023.binominalSubjectificationSteps : List Traugott2010.SubjectificationStep

Subjectification steps in the binominal (N₁-of-N₂) domain.

Equations

• One or more equations did not get rendered due to their size.

theorem TenWolde2023.binominal_steps_directed (s : Traugott2010.SubjectificationStep) : s ∈ binominalSubjectificationSteps → s.sourceLevel ≤ s.targetLevel

The N+PP → EBNP step is a genuine subjectification (nonSubjective → subjective); the later steps maintain subjectivity while bleaching semantics further.