Documentation

Linglib.Phenomena.Complementation.Studies.Noonan2007

Complementation Bridge Theorems #

Interconnection theorems linking @cite{noonan-2007}'s complementation typology to existing linglib 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

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.

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

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

The mapping uses levinClass, factivePresup, causativeBuilder, implicativeBuilder, cosType, speechActVerb, and attitudeBuilder:

  • levinClass ==.see → perception (see)
  • factivePresup → knowledge (know, realize, regret)
  • causativeBuilder.isSome → manipulative (cause, make, force)
  • implicativeBuilder.isSome → achievement (manage, fail)
  • cosType.isSome → phasal (stop, start, continue)
  • speechActVerb → utterance (say, tell)
  • attitudeBuilder doxastic → propAttitude (believe, think)
  • attitudeBuilder preferential positive → desiderative (want, hope)
  • attitudeBuilder 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.

    source
    theorem Phenomena.Complementation.Bridge.know_is_knowledge :
    deriveCTPClass Fragments.English.Predicates.Verbal.know = some Typology.CTPClass.knowledge
    source
    theorem Phenomena.Complementation.Bridge.regret_is_knowledge :
    deriveCTPClass Fragments.English.Predicates.Verbal.regret = some Typology.CTPClass.knowledge
    source
    theorem Phenomena.Complementation.Bridge.realize_is_knowledge :
    deriveCTPClass Fragments.English.Predicates.Verbal.realize = some Typology.CTPClass.knowledge
    source
    theorem Phenomena.Complementation.Bridge.discover_is_knowledge :
    deriveCTPClass Fragments.English.Predicates.Verbal.discover = some Typology.CTPClass.knowledge
    source
    theorem Phenomena.Complementation.Bridge.notice_is_knowledge :
    deriveCTPClass Fragments.English.Predicates.Verbal.notice = some Typology.CTPClass.knowledge
    source
    theorem Phenomena.Complementation.Bridge.remember_rog_is_knowledge :
    deriveCTPClass Fragments.English.Predicates.Verbal.remember_rog = some Typology.CTPClass.knowledge
    source
    theorem Phenomena.Complementation.Bridge.forget_rog_is_knowledge :
    deriveCTPClass Fragments.English.Predicates.Verbal.forget_rog = some Typology.CTPClass.knowledge
    source
    theorem Phenomena.Complementation.Bridge.see_is_perception :
    deriveCTPClass Fragments.English.Predicates.Verbal.see = some Typology.CTPClass.perception
    source
    theorem Phenomena.Complementation.Bridge.say_is_utterance :
    deriveCTPClass Fragments.English.Predicates.Verbal.say = some Typology.CTPClass.utterance
    source
    theorem Phenomena.Complementation.Bridge.tell_is_utterance :
    deriveCTPClass Fragments.English.Predicates.Verbal.tell = some Typology.CTPClass.utterance
    source
    theorem Phenomena.Complementation.Bridge.claim_is_utterance :
    deriveCTPClass Fragments.English.Predicates.Verbal.claim = some Typology.CTPClass.utterance
    source
    theorem Phenomena.Complementation.Bridge.ask_is_utterance :
    deriveCTPClass Fragments.English.Predicates.Verbal.ask = some Typology.CTPClass.utterance
    source
    theorem Phenomena.Complementation.Bridge.believe_is_propAttitude :
    deriveCTPClass Fragments.English.Predicates.Verbal.believe = some Typology.CTPClass.propAttitude
    source
    theorem Phenomena.Complementation.Bridge.think_is_propAttitude :
    deriveCTPClass Fragments.English.Predicates.Verbal.think = some Typology.CTPClass.propAttitude
    source
    theorem Phenomena.Complementation.Bridge.want_is_desiderative :
    deriveCTPClass Fragments.English.Predicates.Verbal.want = some Typology.CTPClass.desiderative
    source
    theorem Phenomena.Complementation.Bridge.hope_is_desiderative :
    deriveCTPClass Fragments.English.Predicates.Verbal.hope = some Typology.CTPClass.desiderative
    source
    theorem Phenomena.Complementation.Bridge.expect_is_desiderative :
    deriveCTPClass Fragments.English.Predicates.Verbal.expect = some Typology.CTPClass.desiderative
    source
    theorem Phenomena.Complementation.Bridge.wish_is_desiderative :
    deriveCTPClass Fragments.English.Predicates.Verbal.wish = some Typology.CTPClass.desiderative
    source
    theorem Phenomena.Complementation.Bridge.decide_is_desiderative :
    deriveCTPClass Fragments.English.Predicates.Verbal.decide_ = some Typology.CTPClass.desiderative
    source
    theorem Phenomena.Complementation.Bridge.fear_is_propAttitude :
    deriveCTPClass Fragments.English.Predicates.Verbal.fear = some Typology.CTPClass.propAttitude
    source
    theorem Phenomena.Complementation.Bridge.dread_is_propAttitude :
    deriveCTPClass Fragments.English.Predicates.Verbal.dread = some Typology.CTPClass.propAttitude
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    theorem Phenomena.Complementation.Bridge.worry_is_propAttitude :
    deriveCTPClass Fragments.English.Predicates.Verbal.worry = some Typology.CTPClass.propAttitude
    source
    theorem Phenomena.Complementation.Bridge.stop_is_phasal :
    deriveCTPClass Fragments.English.Predicates.Verbal.stop = some Typology.CTPClass.phasal
    source
    theorem Phenomena.Complementation.Bridge.quit_is_phasal :
    deriveCTPClass Fragments.English.Predicates.Verbal.quit = some Typology.CTPClass.phasal
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    theorem Phenomena.Complementation.Bridge.start_is_phasal :
    deriveCTPClass Fragments.English.Predicates.Verbal.start = some Typology.CTPClass.phasal
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    theorem Phenomena.Complementation.Bridge.begin_is_phasal :
    deriveCTPClass Fragments.English.Predicates.Verbal.begin_ = some Typology.CTPClass.phasal
    source
    theorem Phenomena.Complementation.Bridge.continue_is_phasal :
    deriveCTPClass Fragments.English.Predicates.Verbal.continue_ = some Typology.CTPClass.phasal
    source
    theorem Phenomena.Complementation.Bridge.keep_is_phasal :
    deriveCTPClass Fragments.English.Predicates.Verbal.keep = some Typology.CTPClass.phasal
    source
    theorem Phenomena.Complementation.Bridge.cause_is_manipulative :
    deriveCTPClass Fragments.English.Predicates.Verbal.cause = some Typology.CTPClass.manipulative
    source
    theorem Phenomena.Complementation.Bridge.make_is_manipulative :
    deriveCTPClass Fragments.English.Predicates.Verbal.make = some Typology.CTPClass.manipulative
    source
    theorem Phenomena.Complementation.Bridge.let_is_manipulative :
    deriveCTPClass Fragments.English.Predicates.Verbal.let_ = some Typology.CTPClass.manipulative
    source
    theorem Phenomena.Complementation.Bridge.have_caus_is_manipulative :
    deriveCTPClass Fragments.English.Predicates.Verbal.have_caus = some Typology.CTPClass.manipulative
    source
    theorem Phenomena.Complementation.Bridge.get_caus_is_manipulative :
    deriveCTPClass Fragments.English.Predicates.Verbal.get_caus = some Typology.CTPClass.manipulative
    source
    theorem Phenomena.Complementation.Bridge.force_is_manipulative :
    deriveCTPClass Fragments.English.Predicates.Verbal.force = some Typology.CTPClass.manipulative
    source
    theorem Phenomena.Complementation.Bridge.manage_is_achievement :
    deriveCTPClass Fragments.English.Predicates.Verbal.manage = some Typology.CTPClass.achievement
    source
    theorem Phenomena.Complementation.Bridge.fail_is_achievement :
    deriveCTPClass Fragments.English.Predicates.Verbal.fail = some Typology.CTPClass.achievement
    source
    theorem Phenomena.Complementation.Bridge.remember_inf_is_achievement :
    deriveCTPClass Fragments.English.Predicates.Verbal.remember = some Typology.CTPClass.achievement
    source
    theorem Phenomena.Complementation.Bridge.forget_inf_is_achievement :
    deriveCTPClass Fragments.English.Predicates.Verbal.forget = some Typology.CTPClass.achievement
    source
    theorem Phenomena.Complementation.Bridge.sleep_no_ctp :
    deriveCTPClass Fragments.English.Predicates.Verbal.sleep = none
    source
    theorem Phenomena.Complementation.Bridge.run_no_ctp :
    deriveCTPClass Fragments.English.Predicates.Verbal.run = none
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    theorem Phenomena.Complementation.Bridge.arrive_no_ctp :
    deriveCTPClass Fragments.English.Predicates.Verbal.arrive = none
    source
    theorem Phenomena.Complementation.Bridge.eat_no_ctp :
    deriveCTPClass Fragments.English.Predicates.Verbal.eat = none
    source
    theorem Phenomena.Complementation.Bridge.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:

    source
    def Phenomena.Complementation.Bridge.ctpToDefaultSelectionClass :
    Typology.CTPClass → Semantics.Questions.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
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      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.

      source
      theorem Phenomena.Complementation.Bridge.ctp_selection_consistent_know :
      ctpToDefaultSelectionClass Typology.CTPClass.knowledge = Semantics.Questions.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).

      source
      theorem Phenomena.Complementation.Bridge.ctp_selection_consistent_discover :
      ctpToDefaultSelectionClass Typology.CTPClass.knowledge = Semantics.Questions.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.discover
      source
      theorem Phenomena.Complementation.Bridge.ctp_selection_consistent_remember_rog :
      ctpToDefaultSelectionClass Typology.CTPClass.knowledge = Semantics.Questions.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.remember_rog
      source
      theorem Phenomena.Complementation.Bridge.ctp_selection_consistent_forget_rog :
      ctpToDefaultSelectionClass Typology.CTPClass.knowledge = Semantics.Questions.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.forget_rog
      source
      theorem Phenomena.Complementation.Bridge.ctp_selection_consistent_ask :
      ctpToDefaultSelectionClass Typology.CTPClass.utterance = Semantics.Questions.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.

      source
      def Phenomena.Complementation.Bridge.ctpToMoodSelector :
      Typology.CTPClass → Semantics.Mood.MoodSelector

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

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

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

        source
        theorem Phenomena.Complementation.Bridge.irrealis_not_indicative (c : Typology.CTPClass) :
        Typology.ctpRealityStatus c = Typology.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

        source
        def Phenomena.Complementation.Bridge.englishToNoonan :
        Core.Verbs.ComplementType → Option Typology.NoonanCompType

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

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          source
          theorem Phenomena.Complementation.Bridge.clausal_complements_have_noonan_type :
          englishToNoonan Core.Verbs.ComplementType.finiteClause ≠ none ∧ englishToNoonan Core.Verbs.ComplementType.infinitival ≠ none ∧ englishToNoonan Core.Verbs.ComplementType.gerund ≠ none ∧ englishToNoonan Core.Verbs.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.

          source
          def Phenomena.Complementation.Bridge.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.
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            E2. Per-verb mood selector verification #

            source
            theorem Phenomena.Complementation.Bridge.know_selects_indicative :
            deriveMoodSelector Fragments.English.Predicates.Verbal.know = Semantics.Mood.MoodSelector.indicativeSelecting
            source
            theorem Phenomena.Complementation.Bridge.believe_selects_indicative :
            deriveMoodSelector Fragments.English.Predicates.Verbal.believe = Semantics.Mood.MoodSelector.indicativeSelecting
            source
            theorem Phenomena.Complementation.Bridge.think_selects_indicative :
            deriveMoodSelector Fragments.English.Predicates.Verbal.think = Semantics.Mood.MoodSelector.indicativeSelecting
            source
            theorem Phenomena.Complementation.Bridge.realize_selects_indicative :
            deriveMoodSelector Fragments.English.Predicates.Verbal.realize = Semantics.Mood.MoodSelector.indicativeSelecting
            source
            theorem Phenomena.Complementation.Bridge.see_selects_indicative :
            deriveMoodSelector Fragments.English.Predicates.Verbal.see = Semantics.Mood.MoodSelector.indicativeSelecting
            source
            theorem Phenomena.Complementation.Bridge.fear_selects_indicative :
            deriveMoodSelector Fragments.English.Predicates.Verbal.fear = Semantics.Mood.MoodSelector.indicativeSelecting
            source
            theorem Phenomena.Complementation.Bridge.worry_selects_indicative :
            deriveMoodSelector Fragments.English.Predicates.Verbal.worry = Semantics.Mood.MoodSelector.indicativeSelecting
            source
            theorem Phenomena.Complementation.Bridge.want_selects_subjunctive :
            deriveMoodSelector Fragments.English.Predicates.Verbal.want = Semantics.Mood.MoodSelector.subjunctiveSelecting
            source
            theorem Phenomena.Complementation.Bridge.wish_selects_subjunctive :
            deriveMoodSelector Fragments.English.Predicates.Verbal.wish = Semantics.Mood.MoodSelector.subjunctiveSelecting
            source
            theorem Phenomena.Complementation.Bridge.intend_selects_subjunctive :
            deriveMoodSelector Fragments.English.Predicates.Verbal.intend = Semantics.Mood.MoodSelector.subjunctiveSelecting
            source
            theorem Phenomena.Complementation.Bridge.cause_selects_subjunctive :
            deriveMoodSelector Fragments.English.Predicates.Verbal.cause = Semantics.Mood.MoodSelector.subjunctiveSelecting
            source
            theorem Phenomena.Complementation.Bridge.make_selects_subjunctive :
            deriveMoodSelector Fragments.English.Predicates.Verbal.make = Semantics.Mood.MoodSelector.subjunctiveSelecting
            source
            theorem Phenomena.Complementation.Bridge.decide_selects_subjunctive :
            deriveMoodSelector Fragments.English.Predicates.Verbal.decide_ = Semantics.Mood.MoodSelector.subjunctiveSelecting
            source
            theorem Phenomena.Complementation.Bridge.hope_mood_variable :
            deriveMoodSelector Fragments.English.Predicates.Verbal.hope = Semantics.Mood.MoodSelector.crossLinguisticallyVariable
            source
            theorem Phenomena.Complementation.Bridge.expect_mood_variable :
            deriveMoodSelector Fragments.English.Predicates.Verbal.expect = Semantics.Mood.MoodSelector.crossLinguisticallyVariable
            source
            theorem Phenomena.Complementation.Bridge.say_mood_neutral :
            deriveMoodSelector Fragments.English.Predicates.Verbal.say = Semantics.Mood.MoodSelector.moodNeutral
            source
            theorem Phenomena.Complementation.Bridge.tell_mood_neutral :
            deriveMoodSelector Fragments.English.Predicates.Verbal.tell = Semantics.Mood.MoodSelector.moodNeutral
            source
            theorem Phenomena.Complementation.Bridge.stop_mood_neutral :
            deriveMoodSelector Fragments.English.Predicates.Verbal.stop = Semantics.Mood.MoodSelector.moodNeutral
            source
            theorem Phenomena.Complementation.Bridge.start_mood_neutral :
            deriveMoodSelector Fragments.English.Predicates.Verbal.start = Semantics.Mood.MoodSelector.moodNeutral
            source
            theorem Phenomena.Complementation.Bridge.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.

            source
            theorem Phenomena.Complementation.Bridge.ctp_mood_consistent_knowledge :
            ctpToMoodSelector Typology.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.

            source
            theorem Phenomena.Complementation.Bridge.ctp_mood_consistent_propAttitude :
            ctpToMoodSelector Typology.CTPClass.propAttitude = deriveMoodSelector Fragments.English.Predicates.Verbal.believe
            source
            theorem Phenomena.Complementation.Bridge.ctp_mood_consistent_desiderative :
            ctpToMoodSelector Typology.CTPClass.desiderative = deriveMoodSelector Fragments.English.Predicates.Verbal.want
            source
            theorem Phenomena.Complementation.Bridge.ctp_mood_consistent_manipulative :
            ctpToMoodSelector Typology.CTPClass.manipulative = deriveMoodSelector Fragments.English.Predicates.Verbal.cause
            source
            theorem Phenomena.Complementation.Bridge.ctp_mood_consistent_perception :
            ctpToMoodSelector Typology.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
            source
            theorem Phenomena.Complementation.Bridge.know_triple_consistency :
            deriveCTPClass Fragments.English.Predicates.Verbal.know = some Typology.CTPClass.knowledge ∧ Semantics.Questions.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.know = Semantics.Questions.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.

            source
            theorem Phenomena.Complementation.Bridge.believe_triple_consistency :
            deriveCTPClass Fragments.English.Predicates.Verbal.believe = some Typology.CTPClass.propAttitude ∧ Semantics.Questions.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.believe = Semantics.Questions.LeftPeriphery.SelectionClass.uninterrogative ∧ deriveMoodSelector Fragments.English.Predicates.Verbal.believe = Semantics.Mood.MoodSelector.indicativeSelecting

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

            source
            theorem Phenomena.Complementation.Bridge.want_triple_consistency :
            deriveCTPClass Fragments.English.Predicates.Verbal.want = some Typology.CTPClass.desiderative ∧ Semantics.Questions.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.want = Semantics.Questions.LeftPeriphery.SelectionClass.uninterrogative ∧ deriveMoodSelector Fragments.English.Predicates.Verbal.want = Semantics.Mood.MoodSelector.subjunctiveSelecting

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

            source
            theorem Phenomena.Complementation.Bridge.ask_triple_consistency :
            deriveCTPClass Fragments.English.Predicates.Verbal.ask = some Typology.CTPClass.utterance ∧ Semantics.Questions.LeftPeriphery.deriveSelectionClass Fragments.English.Predicates.Verbal.ask = Semantics.Questions.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).

            source
            def Phenomena.Complementation.Bridge.ctpDefaultComplementSize :
            Typology.CTPClass → Minimalism.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
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              source
              theorem Phenomena.Complementation.Bridge.utterance_default_cp :
              ctpDefaultComplementSize Typology.CTPClass.utterance = Minimalism.ComplementSize.cP

              Utterance CTPs default to CP.

              source
              theorem Phenomena.Complementation.Bridge.propAttitude_default_cp :
              ctpDefaultComplementSize Typology.CTPClass.propAttitude = Minimalism.ComplementSize.cP

              Propositional attitude CTPs default to CP.

              source
              theorem Phenomena.Complementation.Bridge.perception_default_tp :
              ctpDefaultComplementSize Typology.CTPClass.perception = Minimalism.ComplementSize.tP

              Perception CTPs default to TP (small clause).

              source
              theorem Phenomena.Complementation.Bridge.phasal_default_vp :
              ctpDefaultComplementSize Typology.CTPClass.phasal = Minimalism.ComplementSize.vP

              Phasal CTPs default to vP (restructuring).

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

              CP-selecting CTPs are opaque to tense Agree.

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

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