Morphological Composition: Phenomena #

@cite{link-1983}

Empirical tests for the Core.Morphology pipeline, verifying that stem-based generation produces correct surface forms and features from real English lexical entries in Fragments/English/.

Coverage #

Regular plurals: dog → dogs, student → students
Irregular plurals: man → men, child → children, person → people
Mass nouns: water, furniture — no plural paradigm
Proper names: John, Mary — no plural paradigm
Verb agreement: sleep → sleeps (vacuous), eat → ate (vacuous)
Vacuity: all verb inflection is semantically vacuous

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theorem Phenomena.Morphology.CompositionBridge.dog_plural_form :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => x.formRule Phenomena.Morphology.CompositionBridge.dogStem✝.lemma_) Phenomena.Morphology.CompositionBridge.dogStem✝¹.paradigm.head? = some "dogs"

Regular plural: "dog" → "dogs"

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theorem Phenomena.Morphology.CompositionBridge.student_plural_form :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => x.formRule Phenomena.Morphology.CompositionBridge.studentStem✝.lemma_) Phenomena.Morphology.CompositionBridge.studentStem✝¹.paradigm.head? = some "students"

Regular plural: "student" → "students"

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theorem Phenomena.Morphology.CompositionBridge.horse_plural_form :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => x.formRule Phenomena.Morphology.CompositionBridge.horseStem✝.lemma_) Phenomena.Morphology.CompositionBridge.horseStem✝¹.paradigm.head? = some "horses"

Regular plural: "horse" → "horses"

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theorem Phenomena.Morphology.CompositionBridge.man_plural_form :

Irregular plural: "man" → "men" (not *"mans")

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theorem Phenomena.Morphology.CompositionBridge.child_plural_form :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => x.formRule Phenomena.Morphology.CompositionBridge.childStem✝.lemma_) Phenomena.Morphology.CompositionBridge.childStem✝¹.paradigm.head? = some "children"

Irregular plural: "child" → "children" (not *"childs")

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theorem Phenomena.Morphology.CompositionBridge.woman_plural_form :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => x.formRule Phenomena.Morphology.CompositionBridge.womanStem✝.lemma_) Phenomena.Morphology.CompositionBridge.womanStem✝¹.paradigm.head? = some "women"

Irregular plural: "woman" → "women"

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theorem Phenomena.Morphology.CompositionBridge.person_plural_form :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => x.formRule Phenomena.Morphology.CompositionBridge.personStem✝.lemma_) Phenomena.Morphology.CompositionBridge.personStem✝¹.paradigm.head? = some "people"

Irregular plural: "person" → "people" (suppletive)

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theorem Phenomena.Morphology.CompositionBridge.fireman_plural_form :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => x.formRule Phenomena.Morphology.CompositionBridge.firemanStem✝.lemma_) Phenomena.Morphology.CompositionBridge.firemanStem✝¹.paradigm.head? = some "firemen"

Irregular plural: "fireman" → "firemen"

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theorem Phenomena.Morphology.CompositionBridge.dog_sg_number :

Phenomena.Morphology.CompositionBridge.dogStem✝.baseFeatures.number = some UD.Number.Sing

Singular base features include number := some.Sing.

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theorem Phenomena.Morphology.CompositionBridge.dog_pl_number :

Option.map (fun (x : Core.Morphology.MorphRule (Unit → Bool)) => (x.featureRule Phenomena.Morphology.CompositionBridge.dogStem✝.baseFeatures).number) Phenomena.Morphology.CompositionBridge.dogStem✝¹.paradigm.head? = some (some UD.Number.Plur)

Plural rule sets number := some.Plur.

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theorem Phenomena.Morphology.CompositionBridge.dog_countable :

Phenomena.Morphology.CompositionBridge.dogStem✝.baseFeatures.countable = some true

Count nouns have countable := some true.

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theorem Phenomena.Morphology.CompositionBridge.water_no_paradigm :

Phenomena.Morphology.CompositionBridge.waterStem✝.paradigm.length = 0

Mass noun "water" has no plural paradigm.

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theorem Phenomena.Morphology.CompositionBridge.furniture_no_paradigm :

Phenomena.Morphology.CompositionBridge.furnitureStem✝.paradigm.length = 0

Mass noun "furniture" has no plural paradigm.

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theorem Phenomena.Morphology.CompositionBridge.rice_no_paradigm :

Phenomena.Morphology.CompositionBridge.riceStem✝.paradigm.length = 0

Mass noun "rice" has no plural paradigm.

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theorem Phenomena.Morphology.CompositionBridge.john_no_paradigm :

Phenomena.Morphology.CompositionBridge.johnStem✝.paradigm.length = 0

Proper name "John" has no inflectional paradigm.

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theorem Phenomena.Morphology.CompositionBridge.john_cat_propn :

Phenomena.Morphology.CompositionBridge.johnStem✝.cat = UD.UPOS.PROPN

Proper names get category PROPN.

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theorem Phenomena.Morphology.CompositionBridge.dog_cat_noun :

Phenomena.Morphology.CompositionBridge.dogStem✝.cat = UD.UPOS.NOUN

Common nouns get category NOUN.

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theorem Phenomena.Morphology.CompositionBridge.john_person :

Phenomena.Morphology.CompositionBridge.johnStem✝.baseFeatures.person = some UD.Person.third

Proper names carry person := some.third.

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theorem Phenomena.Morphology.CompositionBridge.sleep_3sg_form :

Option.map (fun (x : Core.Morphology.MorphRule Unit) => x.formRule Phenomena.Morphology.CompositionBridge.sleepStem✝.lemma_) Phenomena.Morphology.CompositionBridge.sleepStem✝¹.paradigm.head? = some "sleeps"

Verb 3sg: "sleep" → "sleeps"

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theorem Phenomena.Morphology.CompositionBridge.eat_past_form :

Verb past: "eat" → "ate"

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theorem Phenomena.Morphology.CompositionBridge.know_3sg_form :

Option.map (fun (x : Core.Morphology.MorphRule Unit) => x.formRule Phenomena.Morphology.CompositionBridge.knowStem✝.lemma_) Phenomena.Morphology.CompositionBridge.knowStem✝¹.paradigm.head? = some "knows"

Verb 3sg: "know" → "knows"

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theorem Phenomena.Morphology.CompositionBridge.sleep_all_vacuous :

(Phenomena.Morphology.CompositionBridge.sleepStem✝.paradigm.all fun (x : Core.Morphology.MorphRule Unit) => x.isVacuous) = true

All verb inflectional rules are semantically vacuous (per entry).

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theorem Phenomena.Morphology.CompositionBridge.eat_all_vacuous :

(Phenomena.Morphology.CompositionBridge.eatStem✝.paradigm.all fun (x : Core.Morphology.MorphRule Unit) => x.isVacuous) = true

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theorem Phenomena.Morphology.CompositionBridge.know_all_vacuous :

(Phenomena.Morphology.CompositionBridge.knowStem✝.paradigm.all fun (x : Core.Morphology.MorphRule Unit) => x.isVacuous) = true

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theorem Phenomena.Morphology.CompositionBridge.allVerbs_all_vacuous :

(Fragments.English.Predicates.Verbal.allVerbs.all fun (v : Fragments.English.Predicates.Verbal.VerbEntry) => v.toStem.paradigm.all fun (x : Core.Morphology.MorphRule Unit) => x.isVacuous) = true

The vacuity theorem generalizes: it holds for ANY VerbEntry.

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theorem Phenomena.Morphology.CompositionBridge.toStem_lemma_eq_formSg (n : Fragments.English.Nouns.NounEntry) :

n.toStem.lemma_ = n.formSg

NounEntry.toStem preserves the lemma as formSg.

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theorem Phenomena.Morphology.CompositionBridge.countable_noun_one_rule :

Phenomena.Morphology.CompositionBridge.dogStem✝.paradigm.length = 1

Count nouns get exactly one paradigm rule (plural).

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theorem Phenomena.Morphology.CompositionBridge.mass_noun_zero_rules :

Phenomena.Morphology.CompositionBridge.waterStem✝.paradigm.length = 0

Mass nouns get zero paradigm rules.

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theorem Phenomena.Morphology.CompositionBridge.plural_changes_truth_conditions :

∃ (atomPred : Bool → Bool) (closurePred : (Bool → Bool) → Bool → Bool) (pred : Bool → Bool) (x : Bool), (Core.Morphology.Number.pluralNounRule closurePred atomPred).semEffect pred x ≠ pred x

With the mereological plural rule, plural marking is NOT semantically vacuous: there exist predicates and entities for which the plural denotation differs from the base. This witnesses @cite{link-1983}'s point that singular and plural nouns denote distinct sets.

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theorem Phenomena.Morphology.CompositionBridge.flat_plural_vacuous :

Core.Morphology.Number.pluralNounRuleFlat.isVacuous = true

The flat plural rule IS semantically vacuous (for toy models).

The Zwicky & Pullum CliticAffixProfile and the MorphRule framework characterize the same morphological operations from complementary angles:

CliticAffixProfile classifies a morpheme's distributional behavior (paradigm gaps, selection, scope idiosyncrasies)
MorphRule specifies the morpheme's compositional semantics (form rule, feature rule, semantic effect)

The bridge theorems below verify that these independent characterizations agree on whether a morphological operation carries semantic content.

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theorem Phenomena.Morphology.CompositionBridge.plural_affix_semantic_agreement :

ZwickyPullum1983.affixPluralS.classify = Core.Morphology.MorphStatus.inflAffix ∧ (Core.Morphology.Number.pluralNounRule id id).isVacuous = false

The plural -s affix is classified as an inflectional affix by Zwicky's diagnostics, AND is semantically non-vacuous in the MorphRule framework. Both analyses agree that plural marking carries semantic content.

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theorem Phenomena.Morphology.CompositionBridge.past_tense_affix_classification :

ZwickyPullum1983.affixEd.classify = Core.Morphology.MorphStatus.inflAffix ∧ (Fragments.English.Predicates.Verbal.sleep.toStem.paradigm.all fun (x : Core.Morphology.MorphRule Unit) => x.isVacuous) = true

The past tense -ed affix is classified as inflectional by Zwicky's diagnostics. In the MorphRule framework, verb tense inflection is vacuous at the word level (tense semantics is compositional, handled by Semantics.Intensional). This is NOT a disagreement: Zwicky's hasSemanticIdiosyncrasies tracks compositionality failures (like "last" ≠ "most late"), while MorphRule.isVacuous tracks whether the regular semantic contribution is non-trivial.

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theorem Phenomena.Morphology.CompositionBridge.irregular_plurals_match_fragment :

All nouns in the fragment with irregular plurals produce the correct irregular form via toStem, matching the paradigm gaps and idiosyncrasies that Zwicky's criterion B/C predict for inflectional affixes.

The @cite{bybee-1985} relevance hierarchy orders morpheme categories by semantic relevance to the verb stem. Categories with higher relevance rank (e.g., agreement = 8) are less semantically relevant — and therefore more likely to be semantically vacuous.

We verify that MorphRule.isVacuous is consistent with Bybee's predictions: agreement morphology (rank 8, least relevant) is vacuous, while number on nouns (which changes denotation via @cite{link-1983}) is not.

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theorem Phenomena.Morphology.CompositionBridge.agreement_highest_rank_is_vacuous :

(Core.Morphology.Number.verbAgreement3sg Unit).category = Core.Morphology.MorphCategory.agreement ∧ Core.Morphology.MorphCategory.agreement.relevanceRank = 8 ∧ (Core.Morphology.Number.verbAgreement3sg Unit).isVacuous = true

Verb agreement (3sg -s) has category =.agreement, which has the highest relevance rank (= least relevant to verb meaning). This predicts semantic vacuity — and indeed verbAgreement3sg has isVacuous = true.

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theorem Phenomena.Morphology.CompositionBridge.plural_number_not_vacuous :

(Core.Morphology.Number.pluralNounRule id id).category = Core.Morphology.MorphCategory.number ∧ (Core.Morphology.Number.pluralNounRule id id).isVacuous = false

Plural noun marking has category =.number, distinct from .agreement — it changes the noun's denotation. The full mereological rule has isVacuous = false.

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theorem Phenomena.Morphology.CompositionBridge.number_vs_agreement_rank :

Core.Morphology.MorphCategory.number.relevanceRank < Core.Morphology.MorphCategory.agreement.relevanceRank

The .number and .agreement categories have different relevance ranks, reflecting that noun number is semantically contentful while verb agreement is vacuous.

Per-entry regularity verification: changing a verb's isRegular flag breaks exactly one theorem.

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theorem Phenomena.Morphology.CompositionBridge.kick_is_regular :

Fragments.English.Predicates.Verbal.kick.isRegular = true

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theorem Phenomena.Morphology.CompositionBridge.arrive_is_regular :

Fragments.English.Predicates.Verbal.arrive.isRegular = true

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theorem Phenomena.Morphology.CompositionBridge.cause_is_regular :

Fragments.English.Predicates.Verbal.cause.isRegular = true

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theorem Phenomena.Morphology.CompositionBridge.kill_is_regular :

Fragments.English.Predicates.Verbal.kill.isRegular = true

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theorem Phenomena.Morphology.CompositionBridge.believe_is_regular :

Fragments.English.Predicates.Verbal.believe.isRegular = true

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theorem Phenomena.Morphology.CompositionBridge.hope_is_regular :

Fragments.English.Predicates.Verbal.hope.isRegular = true

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theorem Phenomena.Morphology.CompositionBridge.fear_is_regular :

Fragments.English.Predicates.Verbal.fear.isRegular = true

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theorem Phenomena.Morphology.CompositionBridge.sleep_is_irregular :

Fragments.English.Predicates.Verbal.sleep.isRegular = false

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theorem Phenomena.Morphology.CompositionBridge.eat_is_irregular :

Fragments.English.Predicates.Verbal.eat.isRegular = false

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theorem Phenomena.Morphology.CompositionBridge.run_is_irregular :

Fragments.English.Predicates.Verbal.run.isRegular = false

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theorem Phenomena.Morphology.CompositionBridge.give_is_irregular :

Fragments.English.Predicates.Verbal.give.isRegular = false

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theorem Phenomena.Morphology.CompositionBridge.know_is_irregular :

Fragments.English.Predicates.Verbal.know.isRegular = false

Rule-grounding for regular verbs: stored forms match expected output. Concrete string checks close by rfl; changing a verb's stem or form fields breaks exactly the relevant theorem.

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theorem Phenomena.Morphology.CompositionBridge.kick_past_form :

Fragments.English.Predicates.Verbal.kick.formPast = "kicked"

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theorem Phenomena.Morphology.CompositionBridge.kick_3sg_form :

Fragments.English.Predicates.Verbal.kick.form3sg = "kicks"

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theorem Phenomena.Morphology.CompositionBridge.kill_past_form :

Fragments.English.Predicates.Verbal.kill.formPast = "killed"

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theorem Phenomena.Morphology.CompositionBridge.kill_3sg_form :

Fragments.English.Predicates.Verbal.kill.form3sg = "kills"