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Linglib.Phenomena.WordOrder.Studies.Hudson1984

Word Grammar Analysis of Subject-Auxiliary Inversion #

@cite{hudson-1984}

Word Grammar handles inversion via subtype inheritance in a word-class taxonomy (@cite{hudson-1984} pp. 117-118):

  1. Verbs take a subject to their left by default
  2. Auxiliaries inherit this subject/left specification from verb
  3. The interrogative auxiliary is a subtype of auxiliary that locally overrides the subject's direction from left to right
  4. Default inheritance does the rest — no special lexical rule needed

The "inverted auxiliary" is not derived by a transformation or lexical rule that flips a direction. It is simply a different word class — a subtype of auxiliary — with its own word-order specification that overrides the inherited default.

End-to-end chain #

ClauseType → wordClassForClauseType → englishAuxNet → resolveArgStr → satisfiesArgStr

Each tree is licensed (or rejected) by the network, connecting:

Reference: @cite{hudson-1990}, @cite{gibson-2025}

source
def Phenomena.WordOrder.Studies.Hudson1984.johnCanSleepTree :
DepGrammar.DepTree

"John can sleep" - declarative (subject left of aux) John ←subj─ can ─aux→ sleep

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    def Phenomena.WordOrder.Studies.Hudson1984.canJohnSleepTree :
    DepGrammar.DepTree

    "Can John sleep?" - interrogative (subject right of aux) can ─subj→ John └──aux→ sleep

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      def Phenomena.WordOrder.Studies.Hudson1984.whatCanJohnEatTree :
      DepGrammar.DepTree

      "What can John eat?" - Matrix wh-question (inverted) what ←obj─ can ─subj→ John └─aux→ eat

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        def Phenomena.WordOrder.Studies.Hudson1984.whatJohnCanEatTree :
        DepGrammar.DepTree

        "*What John can eat?" - Ungrammatical as matrix question what ←obj─ eat ←aux─ can ←subj─ John

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          def Phenomena.WordOrder.Studies.Hudson1984.canJohnEatPizzaTree :
          DepGrammar.DepTree

          "Can John eat pizza?" - Matrix yes-no question (inverted) can ─subj→ John └─aux→ eat ─obj→ pizza

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            def Phenomena.WordOrder.Studies.Hudson1984.johnCanEatPizzaTree :
            DepGrammar.DepTree

            "*John can eat pizza?" - Ungrammatical as matrix question John ←subj─ can ─aux→ eat ─obj→ pizza

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              Intransitive trees (can + sleep) #

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_licenses_inverted_question :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet canJohnSleepTree 0 ClauseType.matrixQuestion = true

              "Can John sleep?" is licensed as a matrix question via the network.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_rejects_inverted_as_declarative :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet canJohnSleepTree 0 ClauseType.declarative = false

              "Can John sleep?" is rejected as a declarative.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_licenses_declarative :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet johnCanSleepTree 1 ClauseType.declarative = true

              "John can sleep" is licensed as a declarative via the network.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_rejects_declarative_as_question :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet johnCanSleepTree 1 ClauseType.matrixQuestion = false

              "John can sleep" is rejected as a matrix question.

              Wh-question trees (what can John eat) #

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_licenses_wh_question :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet whatCanJohnEatTree 1 ClauseType.matrixQuestion = true

              "What can John eat?" is licensed as a matrix question.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_rejects_wh_noninverted :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet whatJohnCanEatTree 2 ClauseType.matrixQuestion = false

              "*What John can eat?" is rejected as a matrix question.

              Yes-no question trees (can John eat pizza) #

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_licenses_yn_question :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet canJohnEatPizzaTree 0 ClauseType.matrixQuestion = true

              "Can John eat pizza?" is licensed as a matrix question.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.wg_rejects_yn_noninverted :
              DepGrammar.WG.wgLicenses DepGrammar.WG.englishAuxNet johnCanEatPizzaTree 1 ClauseType.matrixQuestion = false

              "*John can eat pizza?" is rejected as a matrix question.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.lexrule_matches_network :
              List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) (DepGrammar.auxInversionRule.transform Phenomena.WordOrder.Studies.Hudson1984.lex_can✝).argStr.slots = List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) (DepGrammar.WG.resolveArgStr DepGrammar.WG.englishAuxNet "interrogative_auxiliary").slots

              The lexical rule's inverted argStr has the same depType+dir projection as the network-derived interrogative auxiliary argStr.

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              theorem Phenomena.WordOrder.Studies.Hudson1984.aux_inv_applies :
              DepGrammar.auxInversionRule.applies Phenomena.WordOrder.Studies.Hudson1984.lex_can✝ = true

              Auxiliary inversion rule applies to non-inverted auxiliaries.

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              theorem Phenomena.WordOrder.Studies.Hudson1984.aux_inv_sets_inv :
              Phenomena.WordOrder.Studies.Hudson1984.lex_can_inv✝.inv = true

              Auxiliary inversion sets the inv feature.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.aux_inv_moves_subj :
              Option.map (fun (x : DepGrammar.ArgSlot) => x.dir) Phenomena.WordOrder.Studies.Hudson1984.lex_can✝.argStr.slots.head? = some DepGrammar.Dir.left ∧ Option.map (fun (x : DepGrammar.ArgSlot) => x.dir) Phenomena.WordOrder.Studies.Hudson1984.lex_can_inv✝.argStr.slots.head? = some DepGrammar.Dir.right

              Auxiliary inversion moves subject from left to right.

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.network_aux_slots_match_manual :
              List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) (DepGrammar.WG.resolveArgStr DepGrammar.WG.englishAuxNet "auxiliary").slots = List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) DepGrammar.argStr_Aux.slots

              Network-derived auxiliary slots agree with manual argStr_Aux on depType and dir (the fields satisfiesArgStr checks).

              source
              theorem Phenomena.WordOrder.Studies.Hudson1984.network_inv_aux_slots_match_manual :
              List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) (DepGrammar.WG.resolveArgStr DepGrammar.WG.englishAuxNet "interrogative_auxiliary").slots = List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) DepGrammar.argStr_AuxInv.slots

              Same for the interrogative (inverted) auxiliary.

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              theorem Phenomena.WordOrder.Studies.Hudson1984.fragment_transitive_matches_network :
              Option.map (fun (x : DepGrammar.ArgStr) => List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) x.slots) (DepGrammar.valenceToArgStr Valence.transitive) = some (List.map (fun (s : DepGrammar.ArgSlot) => (s.depType, s.dir)) (DepGrammar.WG.resolveArgStr DepGrammar.WG.englishAuxNet "transitive").slots)

              valenceToArgStr .transitive has the same depType+dir projection as the network-derived transitive word class.

              source
              def Phenomena.WordOrder.Studies.Hudson1984.saiContextRequiresInversion :
              SubjectAuxInversion.SAIContext → Bool

              Map SAI contexts to whether they require inversion.

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