Noonan (2007): Complementation Typology + Bridge Theorems

@cite{noonan-2007}

Noonan's complementation typology (six complement types, twelve CTP classes, realis/irrealis split, equi-deletion restriction, indicative implicational hierarchy) plus interconnection theorems linking it to existing linglib infrastructure.

Part I: Per-language CTP data + Noonan's verified generalizations

7-language CTPDatum sample (English/Latin/Turkish/Irish/Persian/Hindi-Urdu/ Japanese) testing four Noonan generalizations:

• G1: Realis/irrealis split (@cite{noonan-2007} Table 2.3)
• G2: Equi-deletion restricted to reduced complement types (§2.1)
• G3: Negative raising restricted to propAttitude/desiderative (gap-filler)
• G4: Per-language indicative-desiderative implies indicative-propAttitude (§2.4)

Part II: Bridge theorems

Five bridges connecting CTPClass to existing infrastructure:

1. CTPClass ↔ VerbEntry (Verbal.lean) — derive CTP class from verb features
2. CTPClass ↔ SelectionClass (LeftPeriphery.lean) — map CTP to question embedding
3. CTPClass ↔ MoodSelector (Mood/Basic.lean) — map CTP to mood selection
4. ComplementType ↔ NoonanCompType — map English-specific to typological categories
5. VerbEntry → MoodSelector — derive mood selection from verb features

English (@cite{noonan-2007} §1.1) attests all six complement types.

def Phenomena.Complementation.Studies.Noonan2007.english_say : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_tell : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_believe : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_think : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_regret : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_know : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_realize : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_see : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_want : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_hope : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_wish : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_make : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_persuade : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_manage : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_stop : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_start : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.english_continue : Typology.Complementation.CTPDatum

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Latin uses indicative/subjunctive split along realis/irrealis lines

(@cite{noonan-2007} §1.3). 

def Phenomena.Complementation.Studies.Noonan2007.latin_dicere : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.latin_credere : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.latin_velle : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.latin_iubere : Typology.Complementation.CTPDatum

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Turkish strongly favors nominalized complements

(@cite{noonan-2007} §1.4). 

def Phenomena.Complementation.Studies.Noonan2007.turkish_sanmak : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.turkish_istemek : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.turkish_baslamak : Typology.Complementation.CTPDatum

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Irish: finite/non-finite split with paratactic patterns

(@cite{noonan-2007} §1.5). 

def Phenomena.Complementation.Studies.Noonan2007.irish_abair : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.irish_ceap : Typology.Complementation.CTPDatum

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Persian: clear subjunctive/indicative split along CTP lines

(@cite{noonan-2007} §2.3). 

def Phenomena.Complementation.Studies.Noonan2007.persian_goftan : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.persian_khastan : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.persian_danestan : Typology.Complementation.CTPDatum

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Hindi-Urdu: subjunctive complement with desideratives

(@cite{noonan-2007} §2.3). 

def Phenomena.Complementation.Studies.Noonan2007.hindi_urdu_sochna : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.hindi_urdu_jaanna : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.hindi_urdu_chaahna : Typology.Complementation.CTPDatum

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Japanese: extensive nominalized complements.

def Phenomena.Complementation.Studies.Noonan2007.japanese_omou : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.japanese_shiru : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.japanese_hoshii : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.japanese_hajimeru : Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.allEnglishCTPData : List Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.allLatinCTPData : List Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.allTurkishCTPData : List Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.allIrishCTPData : List Typology.Complementation.CTPDatum

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• Phenomena.Complementation.Studies.Noonan2007.allIrishCTPData = [Phenomena.Complementation.Studies.Noonan2007.irish_abair, Phenomena.Complementation.Studies.Noonan2007.irish_ceap]

def Phenomena.Complementation.Studies.Noonan2007.allPersianCTPData : List Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.allHindiUrduCTPData : List Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.allJapaneseCTPData : List Typology.Complementation.CTPDatum

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def Phenomena.Complementation.Studies.Noonan2007.allCTPData : List Typology.Complementation.CTPDatum

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theorem Phenomena.Complementation.Studies.Noonan2007.realis_classes : Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.utterance = Typology.Complementation.RealityStatus.realis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.propAttitude = Typology.Complementation.RealityStatus.realis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.commentative = Typology.Complementation.RealityStatus.realis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.knowledge = Typology.Complementation.RealityStatus.realis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.perception = Typology.Complementation.RealityStatus.realis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.phasal = Typology.Complementation.RealityStatus.realis

theorem Phenomena.Complementation.Studies.Noonan2007.irrealis_classes : Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.desiderative = Typology.Complementation.RealityStatus.irrealis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.manipulative = Typology.Complementation.RealityStatus.irrealis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.modal = Typology.Complementation.RealityStatus.irrealis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.achievement = Typology.Complementation.RealityStatus.irrealis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.pretence = Typology.Complementation.RealityStatus.irrealis ∧ Typology.Complementation.ctpRealityStatus Typology.Complementation.CTPClass.negative = Typology.Complementation.RealityStatus.irrealis

theorem Phenomena.Complementation.Studies.Noonan2007.reality_status_consistent (d : Typology.Complementation.CTPDatum) : d ∈ allCTPData → d.realityStatus = Typology.Complementation.ctpRealityStatus d.ctpClass

Each datum's reality status matches the CTP class's default.

theorem Phenomena.Complementation.Studies.Noonan2007.equi_requires_reduced (d : Typology.Complementation.CTPDatum) : d ∈ allCTPData → d.hasEquiDeletion = true → d.allowedCompTypes.any Typology.Complementation.NoonanCompType.isReduced = true

Equi-deletion only occurs when some allowed complement type is reduced.

theorem Phenomena.Complementation.Studies.Noonan2007.negative_raising_class_restriction (d : Typology.Complementation.CTPDatum) : d ∈ allCTPData → d.hasNegativeRaising = true → d.ctpClass = Typology.Complementation.CTPClass.propAttitude ∨ d.ctpClass = Typology.Complementation.CTPClass.desiderative

Negative raising verbs are exclusively propAttitude or desiderative.

theorem Phenomena.Complementation.Studies.Noonan2007.knowledge_no_negative_raising (d : Typology.Complementation.CTPDatum) : d ∈ allCTPData → d.ctpClass = Typology.Complementation.CTPClass.knowledge → d.hasNegativeRaising = false

Knowledge CTPs never support negative raising.

def Phenomena.Complementation.Studies.Noonan2007.languageHasIndicativeDesiderative (data : List Typology.Complementation.CTPDatum) (lang : String) : Bool

Does this language use indicative with desideratives?

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def Phenomena.Complementation.Studies.Noonan2007.languageHasIndicativePropAttitude (data : List Typology.Complementation.CTPDatum) (lang : String) : Bool

Does this language use indicative with propAttitudes?

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theorem Phenomena.Complementation.Studies.Noonan2007.indicative_hierarchy_english : languageHasIndicativeDesiderative allCTPData "English" = true → languageHasIndicativePropAttitude allCTPData "English" = true

Implicational hierarchy per-language (@cite{noonan-2007} §2.4): if a language uses indicative for desiderative CTPs, it also uses indicative for propositional-attitude CTPs.

English is the only language in the sample with indicative-desiderative (hope and wish), so English is the only place this implication has nontrivial content. The 6 other-language theorems were vacuously true (false antecedent) and have been deleted. To extend this generalization further, add a language with indicative-desiderative attestation (Modern Greek thélo na + indicative-mood form; Bulgarian iskam da + present-indicative form).

A1. Derive CTPClass from VerbEntry fields

CTPClass is DERIVED from existing VerbEntry fields — not added as a new field. This follows the deriveSelectionClass pattern from LeftPeriphery.lean.

def Phenomena.Complementation.Studies.Noonan2007.deriveCTPClass (v : Fragments.English.Predicates.Verbal.VerbEntry) : Option Typology.Complementation.CTPClass

Derive Noonan's CTP class from a VerbEntry's primitive fields.

The mapping uses levinClass, factivePresup, causative, implicative, cosType, speechActVerb, and attitude:

• levinClass ==.see → perception (see)
• factivePresup → knowledge (know, realize, regret)
• causative.isSome → manipulative (cause, make, force)
• implicative.isSome → achievement (manage, fail)
• cosType.isSome → phasal (stop, start, continue)
• speechActVerb → utterance (say, tell)
• attitude doxastic → propAttitude (believe, think)
• attitude preferential positive → desiderative (want, hope)
• attitude preferential other → propAttitude (fear, worry)
• Otherwise → none

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A2. Per-verb verification theorems

Each theorem is proved by native_decide. Changing one VerbEntry field breaks exactly one theorem.

theorem Phenomena.Complementation.Studies.Noonan2007.know_is_knowledge : deriveCTPClass Fragments.English.Predicates.Verbal.know = some Typology.Complementation.CTPClass.knowledge

theorem Phenomena.Complementation.Studies.Noonan2007.regret_is_knowledge : deriveCTPClass Fragments.English.Predicates.Verbal.regret = some Typology.Complementation.CTPClass.knowledge

theorem Phenomena.Complementation.Studies.Noonan2007.realize_is_knowledge : deriveCTPClass Fragments.English.Predicates.Verbal.realize = some Typology.Complementation.CTPClass.knowledge

theorem Phenomena.Complementation.Studies.Noonan2007.discover_is_knowledge : deriveCTPClass Fragments.English.Predicates.Verbal.discover = some Typology.Complementation.CTPClass.knowledge

theorem Phenomena.Complementation.Studies.Noonan2007.notice_is_knowledge : deriveCTPClass Fragments.English.Predicates.Verbal.notice = some Typology.Complementation.CTPClass.knowledge

theorem Phenomena.Complementation.Studies.Noonan2007.remember_rog_is_knowledge : deriveCTPClass Fragments.English.Predicates.Verbal.remember_rog = some Typology.Complementation.CTPClass.knowledge

theorem Phenomena.Complementation.Studies.Noonan2007.forget_rog_is_knowledge : deriveCTPClass Fragments.English.Predicates.Verbal.forget_rog = some Typology.Complementation.CTPClass.knowledge

theorem Phenomena.Complementation.Studies.Noonan2007.see_is_perception : deriveCTPClass Fragments.English.Predicates.Verbal.see = some Typology.Complementation.CTPClass.perception

theorem Phenomena.Complementation.Studies.Noonan2007.say_is_utterance : deriveCTPClass Fragments.English.Predicates.Verbal.say = some Typology.Complementation.CTPClass.utterance

theorem Phenomena.Complementation.Studies.Noonan2007.tell_is_utterance : deriveCTPClass Fragments.English.Predicates.Verbal.tell = some Typology.Complementation.CTPClass.utterance

theorem Phenomena.Complementation.Studies.Noonan2007.claim_is_utterance : deriveCTPClass Fragments.English.Predicates.Verbal.claim = some Typology.Complementation.CTPClass.utterance

theorem Phenomena.Complementation.Studies.Noonan2007.ask_is_utterance : deriveCTPClass Fragments.English.Predicates.Verbal.ask = some Typology.Complementation.CTPClass.utterance

theorem Phenomena.Complementation.Studies.Noonan2007.believe_is_propAttitude : deriveCTPClass Fragments.English.Predicates.Verbal.believe = some Typology.Complementation.CTPClass.propAttitude

theorem Phenomena.Complementation.Studies.Noonan2007.think_is_propAttitude : deriveCTPClass Fragments.English.Predicates.Verbal.think = some Typology.Complementation.CTPClass.propAttitude

theorem Phenomena.Complementation.Studies.Noonan2007.want_is_desiderative : deriveCTPClass Fragments.English.Predicates.Verbal.want = some Typology.Complementation.CTPClass.desiderative

theorem Phenomena.Complementation.Studies.Noonan2007.hope_is_desiderative : deriveCTPClass Fragments.English.Predicates.Verbal.hope = some Typology.Complementation.CTPClass.desiderative

theorem Phenomena.Complementation.Studies.Noonan2007.expect_is_desiderative : deriveCTPClass Fragments.English.Predicates.Verbal.expect = some Typology.Complementation.CTPClass.desiderative

theorem Phenomena.Complementation.Studies.Noonan2007.wish_is_desiderative : deriveCTPClass Fragments.English.Predicates.Verbal.wish = some Typology.Complementation.CTPClass.desiderative

theorem Phenomena.Complementation.Studies.Noonan2007.decide_is_desiderative : deriveCTPClass Fragments.English.Predicates.Verbal.decide_ = some Typology.Complementation.CTPClass.desiderative

theorem Phenomena.Complementation.Studies.Noonan2007.fear_is_propAttitude : deriveCTPClass Fragments.English.Predicates.Verbal.fear = some Typology.Complementation.CTPClass.propAttitude

theorem Phenomena.Complementation.Studies.Noonan2007.dread_is_propAttitude : deriveCTPClass Fragments.English.Predicates.Verbal.dread = some Typology.Complementation.CTPClass.propAttitude

theorem Phenomena.Complementation.Studies.Noonan2007.worry_is_propAttitude : deriveCTPClass Fragments.English.Predicates.Verbal.worry = some Typology.Complementation.CTPClass.propAttitude

theorem Phenomena.Complementation.Studies.Noonan2007.stop_is_phasal : deriveCTPClass Fragments.English.Predicates.Verbal.stop = some Typology.Complementation.CTPClass.phasal

theorem Phenomena.Complementation.Studies.Noonan2007.quit_is_phasal : deriveCTPClass Fragments.English.Predicates.Verbal.quit = some Typology.Complementation.CTPClass.phasal

theorem Phenomena.Complementation.Studies.Noonan2007.start_is_phasal : deriveCTPClass Fragments.English.Predicates.Verbal.start = some Typology.Complementation.CTPClass.phasal

theorem Phenomena.Complementation.Studies.Noonan2007.begin_is_phasal : deriveCTPClass Fragments.English.Predicates.Verbal.begin_ = some Typology.Complementation.CTPClass.phasal

theorem Phenomena.Complementation.Studies.Noonan2007.continue_is_phasal : deriveCTPClass Fragments.English.Predicates.Verbal.continue_ = some Typology.Complementation.CTPClass.phasal

theorem Phenomena.Complementation.Studies.Noonan2007.keep_is_phasal : deriveCTPClass Fragments.English.Predicates.Verbal.keep = some Typology.Complementation.CTPClass.phasal

theorem Phenomena.Complementation.Studies.Noonan2007.cause_is_manipulative : deriveCTPClass Fragments.English.Predicates.Verbal.cause = some Typology.Complementation.CTPClass.manipulative

theorem Phenomena.Complementation.Studies.Noonan2007.make_is_manipulative : deriveCTPClass Fragments.English.Predicates.Verbal.make = some Typology.Complementation.CTPClass.manipulative

theorem Phenomena.Complementation.Studies.Noonan2007.let_is_manipulative : deriveCTPClass Fragments.English.Predicates.Verbal.let_ = some Typology.Complementation.CTPClass.manipulative

theorem Phenomena.Complementation.Studies.Noonan2007.have_caus_is_manipulative : deriveCTPClass Fragments.English.Predicates.Verbal.have_caus = some Typology.Complementation.CTPClass.manipulative

theorem Phenomena.Complementation.Studies.Noonan2007.get_caus_is_manipulative : deriveCTPClass Fragments.English.Predicates.Verbal.get_caus = some Typology.Complementation.CTPClass.manipulative

theorem Phenomena.Complementation.Studies.Noonan2007.force_is_manipulative : deriveCTPClass Fragments.English.Predicates.Verbal.force = some Typology.Complementation.CTPClass.manipulative

theorem Phenomena.Complementation.Studies.Noonan2007.manage_is_achievement : deriveCTPClass Fragments.English.Predicates.Verbal.manage = some Typology.Complementation.CTPClass.achievement

theorem Phenomena.Complementation.Studies.Noonan2007.fail_is_achievement : deriveCTPClass Fragments.English.Predicates.Verbal.fail = some Typology.Complementation.CTPClass.achievement

theorem Phenomena.Complementation.Studies.Noonan2007.remember_inf_is_achievement : deriveCTPClass Fragments.English.Predicates.Verbal.remember = some Typology.Complementation.CTPClass.achievement

theorem Phenomena.Complementation.Studies.Noonan2007.forget_inf_is_achievement : deriveCTPClass Fragments.English.Predicates.Verbal.forget = some Typology.Complementation.CTPClass.achievement

theorem Phenomena.Complementation.Studies.Noonan2007.sleep_no_ctp : deriveCTPClass Fragments.English.Predicates.Verbal.sleep = none

theorem Phenomena.Complementation.Studies.Noonan2007.run_no_ctp : deriveCTPClass Fragments.English.Predicates.Verbal.run = none

theorem Phenomena.Complementation.Studies.Noonan2007.arrive_no_ctp : deriveCTPClass Fragments.English.Predicates.Verbal.arrive = none

theorem Phenomena.Complementation.Studies.Noonan2007.eat_no_ctp : deriveCTPClass Fragments.English.Predicates.Verbal.eat = none

theorem Phenomena.Complementation.Studies.Noonan2007.kick_no_ctp : deriveCTPClass Fragments.English.Predicates.Verbal.kick = none

B1. Map Noonan's CTP classes to Dayal's selection classes

This connects two independent typological systems:

• @cite{noonan-2007}: CTP semantics → complement type
• @cite{dayal-2025}: Predicate semantics → left-peripheral selection

def Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass : Typology.Complementation.CTPClass → Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass

Default mapping from CTP class to selection class.

• Knowledge → responsive (know, remember: entail knowledge of answer)
• Utterance → rogativeSAP (ask, tell: speech-act layer)
• PropAttitude → uninterrogative (believe, think: no question embedding)
• Desiderative → uninterrogative (want, hope: anti-rogative)
• Perception → responsive (see: factive perception of answer)
• Achievement → uninterrogative (manage: no question embedding)
• Phasal → uninterrogative (stop: no question embedding)
• Manipulative → uninterrogative (make: no question embedding)
• Others → uninterrogative

Equations

• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.knowledge = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.responsive
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.utterance = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.rogativeSAP
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.propAttitude = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.desiderative = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.perception = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.responsive
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.achievement = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.phasal = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.manipulative = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.commentative = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.pretence = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.modal = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative
• Phenomena.Complementation.Studies.Noonan2007.ctpToDefaultSelectionClass Typology.Complementation.CTPClass.negative = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative

B2. Consistency with deriveSelectionClass

Verify that for verbs where CTP class is defined AND the verb takes questions, the two derivations agree. Note: many CTPs don't embed questions at all, so the comparison is only meaningful for question-taking verbs.

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_selection_consistent_know : ctpToDefaultSelectionClass Typology.Complementation.CTPClass.knowledge = Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.know

For question-embedding verbs with a CTP class, the CTP-based mapping matches the structural derivation from LeftPeriphery.lean.

This covers: know, discover, remember_rog, forget_rog (knowledge → responsive), ask (utterance → rogativeSAP).

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_selection_consistent_discover : ctpToDefaultSelectionClass Typology.Complementation.CTPClass.knowledge = Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.discover

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_selection_consistent_remember_rog : ctpToDefaultSelectionClass Typology.Complementation.CTPClass.knowledge = Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.remember_rog

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_selection_consistent_forget_rog : ctpToDefaultSelectionClass Typology.Complementation.CTPClass.knowledge = Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.forget_rog

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_selection_consistent_ask : ctpToDefaultSelectionClass Typology.Complementation.CTPClass.utterance = Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.ask

C1. Map CTP classes to mood selection

This connects Noonan's semantic CTP classes to @cite{mendes-2025}'s mood semantics. The realis/irrealis split predicts mood selection.

def Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector : Typology.Complementation.CTPClass → Semantics.Mood.MoodSelector

Map CTP class to mood selection. Realis CTPs select indicative; irrealis select subjunctive. Some are language-dependent (moodNeutral).

Equations

• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.knowledge = Semantics.Mood.MoodSelector.indicativeSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.utterance = Semantics.Mood.MoodSelector.moodNeutral
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.propAttitude = Semantics.Mood.MoodSelector.indicativeSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.commentative = Semantics.Mood.MoodSelector.indicativeSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.perception = Semantics.Mood.MoodSelector.indicativeSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.desiderative = Semantics.Mood.MoodSelector.subjunctiveSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.manipulative = Semantics.Mood.MoodSelector.subjunctiveSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.modal = Semantics.Mood.MoodSelector.subjunctiveSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.achievement = Semantics.Mood.MoodSelector.moodNeutral
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.phasal = Semantics.Mood.MoodSelector.moodNeutral
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.pretence = Semantics.Mood.MoodSelector.subjunctiveSelecting
• Phenomena.Complementation.Studies.Noonan2007.ctpToMoodSelector Typology.Complementation.CTPClass.negative = Semantics.Mood.MoodSelector.subjunctiveSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.realis_not_subjunctive (c : Typology.Complementation.CTPClass) : Typology.Complementation.ctpRealityStatus c = Typology.Complementation.RealityStatus.realis → ctpToMoodSelector c ≠ Semantics.Mood.MoodSelector.subjunctiveSelecting

Realis CTPs select indicative or are mood-neutral (never subjunctive-selecting).

theorem Phenomena.Complementation.Studies.Noonan2007.irrealis_not_indicative (c : Typology.Complementation.CTPClass) : Typology.Complementation.ctpRealityStatus c = Typology.Complementation.RealityStatus.irrealis → ctpToMoodSelector c ≠ Semantics.Mood.MoodSelector.indicativeSelecting

Irrealis CTPs select subjunctive or are mood-neutral (never indicative-selecting).

D1. Map linglib's English-specific complement types to Noonan's

typological categories

def Phenomena.Complementation.Studies.Noonan2007.englishToNoonan : Semantics.Lexical.ComplementType → Option Typology.Complementation.NoonanCompType

Map English fragment complement types to Noonan's universal categories. Returns none for types that don't correspond to a clausal complement.

Equations

• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.finiteClause = some Typology.Complementation.NoonanCompType.indicative
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.infinitival = some Typology.Complementation.NoonanCompType.infinitive
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.gerund = some Typology.Complementation.NoonanCompType.nominalized
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.smallClause = some Typology.Complementation.NoonanCompType.paratactic
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.none = none
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.np = none
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.np_np = none
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.np_pp = none
• Phenomena.Complementation.Studies.Noonan2007.englishToNoonan Semantics.Lexical.ComplementType.question = some Typology.Complementation.NoonanCompType.indicative

theorem Phenomena.Complementation.Studies.Noonan2007.clausal_complements_have_noonan_type : englishToNoonan Semantics.Lexical.ComplementType.finiteClause ≠ none ∧ englishToNoonan Semantics.Lexical.ComplementType.infinitival ≠ none ∧ englishToNoonan Semantics.Lexical.ComplementType.gerund ≠ none ∧ englishToNoonan Semantics.Lexical.ComplementType.smallClause ≠ none

Every English verb that takes a clausal complement maps to a Noonan type.

E1. Derive MoodSelector from VerbEntry fields

This is placed in Bridge.lean (not Verbal.lean) to avoid circular imports: it needs both Verbal and Mood/Basic. Follows the deriveSelectionClass pattern.

def Phenomena.Complementation.Studies.Noonan2007.deriveMoodSelector (v : Fragments.English.Predicates.Verbal.VerbEntry) : Semantics.Mood.MoodSelector

Derive mood selection from a VerbEntry's primitive fields.

The logic:

• Preferential positive + Levin want-class → subjunctive (want, wish)
• Preferential positive + non-want-class → crossLinguisticallyVariable (hope, expect: SBJV in some languages, IND in others; @cite{grano-2024} Table 1)
• Preferential negative/uncertainty attitude → indicative (fear, worry)
• Doxastic attitude → indicative (believe, think)
• Factive → indicative (know: presupposes truth)
• Perception (levinClass ==.see) → indicative (see)
• Speech-act verb → moodNeutral (say: varies cross-linguistically)
• Change-of-state → moodNeutral (stop: varies)
• Causative → subjunctive (make: irrealis)
• Implicative → moodNeutral (manage: varies)
• Otherwise → moodNeutral

Equations

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

E2. Per-verb mood selector verification

theorem Phenomena.Complementation.Studies.Noonan2007.know_selects_indicative : deriveMoodSelector Fragments.English.Predicates.Verbal.know = Semantics.Mood.MoodSelector.indicativeSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.believe_selects_indicative : deriveMoodSelector Fragments.English.Predicates.Verbal.believe = Semantics.Mood.MoodSelector.indicativeSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.think_selects_indicative : deriveMoodSelector Fragments.English.Predicates.Verbal.think = Semantics.Mood.MoodSelector.indicativeSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.realize_selects_indicative : deriveMoodSelector Fragments.English.Predicates.Verbal.realize = Semantics.Mood.MoodSelector.indicativeSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.see_selects_indicative : deriveMoodSelector Fragments.English.Predicates.Verbal.see = Semantics.Mood.MoodSelector.indicativeSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.fear_selects_indicative : deriveMoodSelector Fragments.English.Predicates.Verbal.fear = Semantics.Mood.MoodSelector.indicativeSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.worry_selects_indicative : deriveMoodSelector Fragments.English.Predicates.Verbal.worry = Semantics.Mood.MoodSelector.indicativeSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.want_selects_subjunctive : deriveMoodSelector Fragments.English.Predicates.Verbal.want = Semantics.Mood.MoodSelector.subjunctiveSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.wish_selects_subjunctive : deriveMoodSelector Fragments.English.Predicates.Verbal.wish = Semantics.Mood.MoodSelector.subjunctiveSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.intend_selects_subjunctive : deriveMoodSelector Fragments.English.Predicates.Verbal.intend = Semantics.Mood.MoodSelector.subjunctiveSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.cause_selects_subjunctive : deriveMoodSelector Fragments.English.Predicates.Verbal.cause = Semantics.Mood.MoodSelector.subjunctiveSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.make_selects_subjunctive : deriveMoodSelector Fragments.English.Predicates.Verbal.make = Semantics.Mood.MoodSelector.subjunctiveSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.decide_selects_subjunctive : deriveMoodSelector Fragments.English.Predicates.Verbal.decide_ = Semantics.Mood.MoodSelector.subjunctiveSelecting

theorem Phenomena.Complementation.Studies.Noonan2007.hope_mood_variable : deriveMoodSelector Fragments.English.Predicates.Verbal.hope = Semantics.Mood.MoodSelector.crossLinguisticallyVariable

theorem Phenomena.Complementation.Studies.Noonan2007.expect_mood_variable : deriveMoodSelector Fragments.English.Predicates.Verbal.expect = Semantics.Mood.MoodSelector.crossLinguisticallyVariable

theorem Phenomena.Complementation.Studies.Noonan2007.say_mood_neutral : deriveMoodSelector Fragments.English.Predicates.Verbal.say = Semantics.Mood.MoodSelector.moodNeutral

theorem Phenomena.Complementation.Studies.Noonan2007.tell_mood_neutral : deriveMoodSelector Fragments.English.Predicates.Verbal.tell = Semantics.Mood.MoodSelector.moodNeutral

theorem Phenomena.Complementation.Studies.Noonan2007.stop_mood_neutral : deriveMoodSelector Fragments.English.Predicates.Verbal.stop = Semantics.Mood.MoodSelector.moodNeutral

theorem Phenomena.Complementation.Studies.Noonan2007.start_mood_neutral : deriveMoodSelector Fragments.English.Predicates.Verbal.start = Semantics.Mood.MoodSelector.moodNeutral

theorem Phenomena.Complementation.Studies.Noonan2007.manage_mood_neutral : deriveMoodSelector Fragments.English.Predicates.Verbal.manage = Semantics.Mood.MoodSelector.moodNeutral

F1. CTP class → mood selector consistency

For verbs with a derivable CTP class, the mood selector derived directly from VerbEntry should be consistent with the CTP-based derivation.

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_mood_consistent_knowledge : ctpToMoodSelector Typology.Complementation.CTPClass.knowledge = deriveMoodSelector Fragments.English.Predicates.Verbal.know

The CTP-based mood mapping agrees with the direct derivation for representative verbs from each CTP class.

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_mood_consistent_propAttitude : ctpToMoodSelector Typology.Complementation.CTPClass.propAttitude = deriveMoodSelector Fragments.English.Predicates.Verbal.believe

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_mood_consistent_desiderative : ctpToMoodSelector Typology.Complementation.CTPClass.desiderative = deriveMoodSelector Fragments.English.Predicates.Verbal.want

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_mood_consistent_manipulative : ctpToMoodSelector Typology.Complementation.CTPClass.manipulative = deriveMoodSelector Fragments.English.Predicates.Verbal.cause

theorem Phenomena.Complementation.Studies.Noonan2007.ctp_mood_consistent_perception : ctpToMoodSelector Typology.Complementation.CTPClass.perception = deriveMoodSelector Fragments.English.Predicates.Verbal.see

F2. Three-way agreement for key verbs

For important verbs, all three classification systems agree:

1. deriveCTPClass → CTP class
2. deriveSelectionClass → question embedding
3. deriveMoodSelector → mood selection

theorem Phenomena.Complementation.Studies.Noonan2007.know_triple_consistency : deriveCTPClass Fragments.English.Predicates.Verbal.know = some Typology.Complementation.CTPClass.knowledge ∧ Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.know = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.responsive ∧ deriveMoodSelector Fragments.English.Predicates.Verbal.know = Semantics.Mood.MoodSelector.indicativeSelecting

"know" is classified consistently across all three bridges: knowledge CTP, responsive selection, indicative mood.

theorem Phenomena.Complementation.Studies.Noonan2007.believe_triple_consistency : deriveCTPClass Fragments.English.Predicates.Verbal.believe = some Typology.Complementation.CTPClass.propAttitude ∧ Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.believe = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative ∧ deriveMoodSelector Fragments.English.Predicates.Verbal.believe = Semantics.Mood.MoodSelector.indicativeSelecting

"believe" is classified consistently: propAttitude CTP, uninterrogative, indicative mood.

theorem Phenomena.Complementation.Studies.Noonan2007.want_triple_consistency : deriveCTPClass Fragments.English.Predicates.Verbal.want = some Typology.Complementation.CTPClass.desiderative ∧ Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.want = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.uninterrogative ∧ deriveMoodSelector Fragments.English.Predicates.Verbal.want = Semantics.Mood.MoodSelector.subjunctiveSelecting

"want" is classified consistently: desiderative CTP, uninterrogative (anti-rogative), subjunctive mood.

theorem Phenomena.Complementation.Studies.Noonan2007.ask_triple_consistency : deriveCTPClass Fragments.English.Predicates.Verbal.ask = some Typology.Complementation.CTPClass.utterance ∧ Interfaces.SyntaxSemantics.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.ask = Interfaces.SyntaxSemantics.LeftPeriphery.SelectionClass.rogativeSAP ∧ deriveMoodSelector Fragments.English.Predicates.Verbal.ask = Semantics.Mood.MoodSelector.moodNeutral

"ask" is classified consistently: utterance CTP, rogativeSAP, mood-neutral.

G1. Complement size by CTP class

@cite{egressy-2026} shows that complement size determines SOT availability in Hungarian. This bridge maps Noonan's CTP classes to their typical complement sizes, connecting the complementation typology to the clause-size infrastructure.

These are default sizes — individual languages may override (e.g., in Hungarian, hogy forces CP regardless of CTP class).

def Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize : Typology.Complementation.CTPClass → Minimalist.ComplementSize

Default complement size for a CTP class.

Finite declarative complements are typically CP-sized. Restructuring predicates select smaller complements.

• utterance → CP (full finite with complementizer)
• propAttitude → CP (full finite that-clause)
• knowledge → CP (factive that-clause)
• perception → TP (small clause / reduced complement)
• desiderative → TP (subjunctive / infinitival)
• manipulative → TP (ECM / small clause)
• phasal → vP (restructuring)
• achievement → vP (restructuring)
• modal → TP (functional, shares T domain)
• commentative → CP (factive that-clause)
• pretence → CP (finite complement)
• negative → vP (restructuring)

Equations

• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.utterance = Minimalist.ComplementSize.cP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.propAttitude = Minimalist.ComplementSize.cP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.knowledge = Minimalist.ComplementSize.cP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.commentative = Minimalist.ComplementSize.cP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.pretence = Minimalist.ComplementSize.cP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.perception = Minimalist.ComplementSize.tP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.desiderative = Minimalist.ComplementSize.tP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.manipulative = Minimalist.ComplementSize.tP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.modal = Minimalist.ComplementSize.tP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.phasal = Minimalist.ComplementSize.vP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.achievement = Minimalist.ComplementSize.vP
• Phenomena.Complementation.Studies.Noonan2007.ctpDefaultComplementSize Typology.Complementation.CTPClass.negative = Minimalist.ComplementSize.vP

theorem Phenomena.Complementation.Studies.Noonan2007.utterance_default_cp : ctpDefaultComplementSize Typology.Complementation.CTPClass.utterance = Minimalist.ComplementSize.cP

Utterance CTPs default to CP.

theorem Phenomena.Complementation.Studies.Noonan2007.propAttitude_default_cp : ctpDefaultComplementSize Typology.Complementation.CTPClass.propAttitude = Minimalist.ComplementSize.cP

Propositional attitude CTPs default to CP.

theorem Phenomena.Complementation.Studies.Noonan2007.perception_default_tp : ctpDefaultComplementSize Typology.Complementation.CTPClass.perception = Minimalist.ComplementSize.tP

Perception CTPs default to TP (small clause).

theorem Phenomena.Complementation.Studies.Noonan2007.phasal_default_vp : ctpDefaultComplementSize Typology.Complementation.CTPClass.phasal = Minimalist.ComplementSize.vP

Phasal CTPs default to vP (restructuring).

theorem Phenomena.Complementation.Studies.Noonan2007.cp_ctps_opaque : (ctpDefaultComplementSize Typology.Complementation.CTPClass.utterance).transparentToTenseAgree = false ∧ (ctpDefaultComplementSize Typology.Complementation.CTPClass.propAttitude).transparentToTenseAgree = false ∧ (ctpDefaultComplementSize Typology.Complementation.CTPClass.knowledge).transparentToTenseAgree = false

CP-selecting CTPs are opaque to tense Agree.

theorem Phenomena.Complementation.Studies.Noonan2007.small_ctps_transparent : (ctpDefaultComplementSize Typology.Complementation.CTPClass.perception).transparentToTenseAgree = true ∧ (ctpDefaultComplementSize Typology.Complementation.CTPClass.desiderative).transparentToTenseAgree = true ∧ (ctpDefaultComplementSize Typology.Complementation.CTPClass.phasal).transparentToTenseAgree = true

TP-selecting and vP-selecting CTPs are transparent to tense Agree.