Documentation

Studies.Bybee1985

Bybee 1985: relevance and lexical strength #

A morpheme category whose meaning is more relevant to the verb stem should have morphological expression, inflectional or derivational, in more languages, sit closer to the stem where it is, and fuse with it more tightly; whether the expression is inflectional depends on generality as well, which works against the most relevant categories. This file formalizes the evidence for the first two predictions, from a fifty-language stratified sample: the frequency surveys of chapter 2 and the morpheme-order counts of the same chapter, in which every tested pair confirms the predicted direction and aspect against tense and against mood does so without a single counterexample.

The order those counts determine is then shown to be the relevance hierarchy's order rather than a table chosen to match it: on the four categories the survey covers, the relation derived from the counts and the hierarchy's order are the same. Fusion, the third claim, is qualitative in the source.

Chapter 5's notion of lexical strength closes the file: an irregular verb keeps its irregularity where its token frequency is high, and the Strong Verbs that regularized are the infrequent ones.

Main definitions #

BybeeCategory — the verbal-inflectional categories of Ch 2, in relevance order.
inflectionalCount50, derivOrInflCount50 — the Ch 2 §5 frequency surveys (Figs 1+2).
orderPairs — the Ch 2 §6 morpheme-order counts, one OrderPair per tested category pair.
toRelevanceHierarchy — the hierarchy category of each surveyed category.
SurveyedCloser — the stem-proximity order derived from orderPairs.
strongStillStrong, strongRegularized — the Ch 5 §6 strong-verb frequency table.

Main results #

valence_highest_when_derivOrInfl, valence_lowest_when_inflectional — the relevance and generality frequency predictions.
predicted_outnumbers_counter, aspect_categorical_against_tense_and_mood — the order predictions.
survey_order_iso_relevance — on the surveyed categories SurveyedCloser and the hierarchy's < coincide via toRelevanceHierarchy: the hierarchy is the order the §6 survey forces, not a stipulated table.
bybeeSurveyedOrder_respects_hierarchy — the surveyed order is sorted by the hierarchy.
strong_verbs_higher_frequency_than_regularized — the Ch 5 §6 diachronic claim: still-Strong verbs have a strictly higher mean token frequency than the regularized ones.

References #

Verbal categories (Ch 2 §3) #

Bybee's six core categories in relevance order: valence, voice, aspect, tense, mood, agreement (number/person/gender are agreement sub-types).

inductive Bybee1985.BybeeCategory :

Bybee's Ch 2 verbal-inflectional categories, in her relevance order (stem first). Constructor docstrings paraphrase the coding definitions of Ch 2 §4, which distinguish subject, object and indirect-object agreement; Figures 1 and 2 split only person agreement, into "person" (the text's subject agreement) and "person (object)".

valence : BybeeCategory
Differences in the number or role of the arguments the verb stem takes.
voice : BybeeCategory
The perspective from which the situation described by the verb stem is viewed.
aspect : BybeeCategory
The way the internal temporal constituency of the situation is viewed.
tense : BybeeCategory
The situation's placement in time, relative to the moment of speech or some other established point.
mood : BybeeCategory
The way the speaker presents the truth of the proposition: probability, possibility, certainty; evidentials are included under mood.
numberAgr : BybeeCategory
Concord by number with one or more arguments of the verb.
personAgr : BybeeCategory
Concord by person with the subject.
personAgrObj : BybeeCategory
Concord by person with the object.
genderAgr : BybeeCategory
Concord with arguments by lexical class, assigned arbitrarily or by inherent qualities of the referent.

Instances For

@[instance_reducible]

instance Bybee1985.instDecidableEqBybeeCategory :

DecidableEq BybeeCategory

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Bybee1985.instDecidableEqBybeeCategory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Bybee1985.instReprBybeeCategory.repr :

BybeeCategory → ℕ → Std.Format

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

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@[instance_reducible]

instance Bybee1985.instReprBybeeCategory :

Repr BybeeCategory

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Bybee1985.instReprBybeeCategory = { reprPrec := Bybee1985.instReprBybeeCategory.repr }

@[instance_reducible]

instance Bybee1985.instFintypeBybeeCategory :

Fintype BybeeCategory

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

Cross-linguistic frequency (Ch 2 §5, Figs 1+2) #

Fig 1 counts the 50-sample languages with inflectional expression of a category; Fig 2 counts those with inflectional or derivational expression. Counts are integers because the sample is exactly 50 (count = percentage / 2).

def Bybee1985.inflectionalCount50 :

BybeeCategory → ℕ

Languages (of 50) with inflectional expression of c (Fig 1).

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Instances For

def Bybee1985.derivOrInflCount50 :

BybeeCategory → ℕ

Languages (of 50) with inflectional or derivational expression of c (Fig 2). Valence reaches 90% once valence-changing derivation is counted; only Haitian, Karankawa, Navaho, Serbo-Croatian, and Vietnamese lack it.

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theorem Bybee1985.valence_highest_when_derivOrInfl (c : BybeeCategory) :

derivOrInflCount50 c ≤ derivOrInflCount50 BybeeCategory.valence

The relevance prediction, tested on Figure 2, which counts derivational as well as inflectional expression: valence is the most frequent category, reflecting near-universal valence-changing morphology.

theorem Bybee1985.valence_lowest_when_inflectional (c : BybeeCategory) :

inflectionalCount50 BybeeCategory.valence ≤ inflectionalCount50 c

The generality prediction: restricted to inflection, valence is the least frequent category (6%, down from 90%) — generality "predicts fewer inflections among the most highly relevant categories", because highly relevant morphology is rarely obligatory across all stems.

theorem Bybee1985.gender_lowest_when_derivOrInfl (c : BybeeCategory) :

derivOrInflCount50 BybeeCategory.genderAgr ≤ derivOrInflCount50 c

In the deriv+infl survey (Fig 2), gender agreement, the last category of Bybee's diagram of relevance, is the least frequent.

Morpheme order (Ch 2 §6) #

The order prediction: the most relevant categories sit closest to the stem, the least relevant furthest. Bybee tests the four most frequent — aspect, tense, mood, person — counting, per pair, how many languages place one closer than the other. A language with both categories is untestable when the morphemes are portmanteau, on opposite sides of the stem (unless only one is stem-adjacent), or mutually exclusive in one slot; a morpheme expressed by stem modification counts as closer than one expressed by affixation.

structure Bybee1985.OrderPair :

A Ch 2 §6 morpheme-order pair.

closer : BybeeCategory
The category predicted closer to the stem.
further : BybeeCategory
The category predicted further from the stem.
closerCount : ℕ
The languages confirming the predicted order.
furtherCount : ℕ
The languages showing the opposite order.
total : ℕ
The languages having both categories, testable or not.

Instances For

@[instance_reducible]

instance Bybee1985.instReprOrderPair :

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Bybee1985.instReprOrderPair = { reprPrec := Bybee1985.instReprOrderPair.repr }

def Bybee1985.instReprOrderPair.repr :

OrderPair → ℕ → Std.Format

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def Bybee1985.orderPairs :

The six pairs Bybee tests in Ch 2 §6; counts verified against the book, each inline comment quoting its source passage.

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theorem Bybee1985.aspect_categorical_against_tense_and_mood (p : OrderPair) :

p ∈ orderPairs → p.closer = BybeeCategory.aspect → p.further = BybeeCategory.tense ∨ p.further = BybeeCategory.mood → p.furtherCount = 0

Aspect vs. tense and aspect vs. mood are categorical: zero counterexamples in the whole sample, the strongest confirmations Bybee reports.

theorem Bybee1985.mood_person_ordering_is_freest (p : OrderPair) :

p ∈ orderPairs → ∀ q ∈ orderPairs, q.closer = BybeeCategory.mood → p.closer ≠ BybeeCategory.mood → p.furtherCount * q.total < q.furtherCount * p.total

Mood vs. person is the freest pair — "the ordering of mood and person is somewhat freer" — cross-multiplied: every other tested pair has a strictly smaller counterexample rate.

theorem Bybee1985.predicted_outnumbers_counter (p : OrderPair) :

p ∈ orderPairs → p.furtherCount < p.closerCount

In every one of the six pairs the predicted direction outnumbers the counter-direction (Ch 2 §6 summary).

The relevance hierarchy #

The survey codes agreement finer than the hierarchy ranks it: number, person, object person and gender agreement are all the hierarchy's agreement.

def Bybee1985.toRelevanceHierarchy :

BybeeCategory → Morphology.RelevanceHierarchy

The hierarchy category a surveyed category belongs to.

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Grounding the hierarchy in the survey #

On the four categories Bybee surveyed (aspect, tense, mood, person), the hierarchy's order is not a free choice: SurveyedCloser, derived from orderPairs, coincides with the hierarchy's < via toRelevanceHierarchy (survey_order_iso_relevance). So a sortedness check over these categories rests on an order isomorphism, not a stipulated table.

def Bybee1985.SurveyedCloser (a b : BybeeCategory) :

a is surveyed closer to the stem than b when some tested Ch 2 §6 pair predicts a closer than b and the language counts confirm that direction (predicted majority). Derived from orderPairs, not stipulated.

Equations

Bybee1985.SurveyedCloser a b = ∃ p ∈ Bybee1985.orderPairs, p.closer = a ∧ p.further = b ∧ p.furtherCount < p.closerCount

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@[instance_reducible]

instance Bybee1985.instDecidableRelBybeeCategorySurveyedCloser :

DecidableRel SurveyedCloser

Equations

Bybee1985.instDecidableRelBybeeCategorySurveyedCloser x✝¹ x✝ = Bybee1985.instDecidableRelBybeeCategorySurveyedCloser._aux_1 x✝¹ x✝

def Bybee1985.Surveyed (c : BybeeCategory) :

A category is surveyed if it appears in any tested Ch 2 §6 pair.

Equations

Bybee1985.Surveyed c = ∃ p ∈ Bybee1985.orderPairs, p.closer = c ∨ p.further = c

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@[instance_reducible]

instance Bybee1985.instDecidablePredBybeeCategorySurveyed :

DecidablePred Surveyed

Equations

Bybee1985.instDecidablePredBybeeCategorySurveyed x✝ = Bybee1985.instDecidablePredBybeeCategorySurveyed._aux_1 x✝

theorem Bybee1985.surveyedCloser_irrefl (a : BybeeCategory) :

¬SurveyedCloser a a

SurveyedCloser is irreflexive: no tested pair ranks a category against itself.

theorem Bybee1985.surveyedCloser_trans (a b c : BybeeCategory) :

SurveyedCloser a b → SurveyedCloser b c → SurveyedCloser a c

SurveyedCloser is transitive — the §6 survey tested every pair among its categories, so the confirmed dominances compose.

theorem Bybee1985.surveyedCloser_total (a b : BybeeCategory) :

Surveyed a → Surveyed b → a ≠ b → SurveyedCloser a b ∨ SurveyedCloser b a

SurveyedCloser is total on the surveyed categories: any two distinct surveyed categories are ordered by the §6 data in exactly one direction. With irreflexivity and transitivity, the survey alone determines a strict total order on its four categories.

theorem Bybee1985.survey_order_iso_relevance (a b : BybeeCategory) :

Surveyed a → Surveyed b → (SurveyedCloser a b ↔ toRelevanceHierarchy a < toRelevanceHierarchy b)

Order isomorphism: on the surveyed categories, SurveyedCloser and the hierarchy's < coincide via toRelevanceHierarchy. The hierarchy there is not merely consistent with Bybee's evidence — it is the order the §6 survey determines.

def Bybee1985.bybeeSurveyedOrder :

List BybeeCategory

The stem-outward ordering of the surveyed categories — a literal, but validated as fully SurveyedCloser-sorted (bybeeSurveyedOrder_sorted) and exhaustive (bybeeSurveyedOrder_complete).

Equations

Bybee1985.bybeeSurveyedOrder = [Bybee1985.BybeeCategory.aspect, Bybee1985.BybeeCategory.tense, Bybee1985.BybeeCategory.mood, Bybee1985.BybeeCategory.personAgr]

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theorem Bybee1985.bybeeSurveyedOrder_sorted :

List.Pairwise SurveyedCloser bybeeSurveyedOrder

theorem Bybee1985.bybeeSurveyedOrder_complete (c : BybeeCategory) :

Surveyed c → c ∈ bybeeSurveyedOrder

theorem Bybee1985.bybeeSurveyedOrder_respects_hierarchy :

(List.map toRelevanceHierarchy bybeeSurveyedOrder).SortedLE

The data-derived surveyed order is sorted by the relevance hierarchy, closing the loop between Bybee's §6 evidence and the hierarchy.

Lexical strength #

Chapter 5 replaces the question whether an item is in the lexicon with two gradient notions. Each token of use strengthens an item's representation — "etching it with deeper and darker lines each time" — and strength declines with disuse; and items bear semantic and phonological connections to one another, a parallel pair of which constitutes a morphological relation. The consequence tested below is diachronic: an irregular verb survives as irregular where its lexical strength is high.

The table on p. 120 lists the modern descendants of the Class I, II and VII Strong Verbs of [Swe82]'s Anglo-Saxon Primer with their all-forms token frequencies; slit and beat now take the zero allomorph of the past tense.

structure Bybee1985.VerbFrequency :

A verb with its all-forms token frequency, which is what lexical strength amounts to here.

verb : String
The verb, by its modern form.
tokenFreq : ℕ
The all-forms token frequency ([FK82]).

Instances For

@[instance_reducible]

instance Bybee1985.instReprVerbFrequency :

Repr VerbFrequency

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Bybee1985.instReprVerbFrequency = { reprPrec := Bybee1985.instReprVerbFrequency.repr }

def Bybee1985.instReprVerbFrequency.repr :

VerbFrequency → ℕ → Std.Format

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def Bybee1985.strongStillStrong :

List VerbFrequency

The Strong Verbs that have stayed Strong (p. 120), with all-forms token frequencies.

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def Bybee1985.strongRegularized :

List VerbFrequency

The Strong Verbs that have regularized or become Weak (p. 120), with all-forms token frequencies.

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theorem Bybee1985.strong_verbs_higher_frequency_than_regularized :

(List.map (fun (x : VerbFrequency) => x.tokenFreq) strongRegularized).sum * strongStillStrong.length < (List.map (fun (x : VerbFrequency) => x.tokenFreq) strongStillStrong).sum * strongRegularized.length

The mean token frequency of the still-Strong verbs strictly exceeds that of the regularized ones — irregularity survives where lexical strength is high. Stated as the cross-multiplied sum comparison to stay in Nat.