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Studies.Westergaard2009

Westergaard (2009): The Acquisition of Word Order: Micro-Cues, Information Structure, and Economy #

This file formalizes the syntactic model of Westergaard's monograph. Verb second is not one parameter but a setting per clause-type head of a split ForceP, one head per sentence type in root clauses and one each for embedded declaratives and embedded questions, so that a language's grammar is the set of cells, a sentence type in an embedding context, in which the finite verb moves to the left periphery. Her Table 3.1 gives that set for six Germanic varieties. The fragments record, from the reference grammars and from her own descriptions, where verb second is obligatory, optional or excluded, and her binary settings agree with them: each grammar contains the cells where the fragment requires verb second and lies within the cells where it allows it, and for five of the six varieties it is exactly the required cells. What children acquire are micro-cues, pieces of structure stating for one cell what its specifier holds and whether the verb fills its head, and four cues separate the five grammars of her Table 3.2. In the Tromsø dialect the monosyllabic wh-words ka, kem and kor are heads and sit in Int⁰ themselves, which blocks verb movement there; the verb second that still occurs is movement to a lower Top⁰, whose feature a given subject checks from the specifier and a focused subject leaves for the verb, so that these questions are verb second exactly when the subject is new.

Main definitions #

Main results #

Implementation notes #

Westergaard's Fin⁰ and Wh⁰ heads are realized as the embedded root-like cells of Bhatt and Dayal: German complementizer-less verb-second complements and Belfast English embedded inversion are both quasiSubordinated, and her Wh⁰ is the yes/no cell her Belfast example instantiates. Danish is the one variety whose table entry is not the fragment's required set, since only some Danish exclamatives are verb second. The cues (57) and (60) for verb movement to I°, which she motivates with Icelandic, the cue for English inflectional elements, som-insertion, focus-sensitive adverbs, kanskje, and the acquisition chapters are not formalized; the Tromsø rows have no fragment and enter only the wh-word model.

References #

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A verb-second grammar is the set of cells, a sentence type in an embedding context, in which the finite verb moves to the left periphery: Westergaard's clause-type heads.

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    Micro-parameters (Table 3.1) #

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    Standard Norwegian moves the verb to Decl⁰, Int⁰ and Pol⁰.

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      Standard English moves the verb to Int⁰ and Pol⁰.

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        Nordmøre Norwegian moves the verb to Decl⁰ and Pol⁰.

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          Belfast English moves the verb to Int⁰, Pol⁰, Imp⁰ and Wh⁰, the last in an embedded root-like yes/no-question.

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            German moves the verb to Decl⁰, Int⁰, Pol⁰ and, in a complementizer-less embedded declarative, Fin⁰.

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              Danish moves the verb to Decl⁰, Int⁰, Pol⁰ and Excl⁰.

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                Table 3.1 is the required set of the fragment for Standard Norwegian, Standard English, Nordmøre, Belfast English and German.

                Table 3.1's Danish grammar lies between the fragment's required and possible cells, since verb second in some exclamatives only is marked as movement to Excl⁰.

                Micro-cues (§4) #

                The specifier of the cue's head holds nothing, a non-subject phrase, or a wh-element.

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                  def Westergaard2009.instReprFiller.repr :
                  Filler → ℕ → Std.Format
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                    A micro-cue: for one cell, what its specifier holds and whether the finite verb fills its head.

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                      def Westergaard2009.instDecidableEqMicroCue.decEq (x✝ x✝¹ : MicroCue) :
                      Decidable (x✝ = x✝¹)
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                          The cue (45) is V2 in wh-questions.

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                            The cue (46) is V2 in declaratives.

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                              The cue (49) is V2 in yes/no-questions.

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                                The cue (52) is V2 in exclamatives.

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                                  The cue (53) is V2 in embedded questions, the embedded root-like yes/no-question of Belfast English.

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                                    The cue (54) is V2 in imperatives.

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                                      The cue (58) is non-V2 in exclamatives.

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                                        The cue (59) is non-V2 in embedded questions.

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                                          A grammar expresses a cue when its setting for the cue's cell is the cue's.

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                                            theorem Westergaard2009.not_expresses_both (lang : V2Grammar) {c c' : MicroCue} (ht : c.target = c'.target) (hv : c.verbInHead ≠ c'.verbInHead) :
                                            ¬(Expresses lang c ∧ Expresses lang c')

                                            A cue and the cue for its absence are never both expressed.

                                            theorem Westergaard2009.table_3_2 :
                                            List.Pairwise (fun (g g' : V2Grammar) => ∃ c ∈ tableCues, ¬(Expresses g c ↔ Expresses g' c)) tableGrammars

                                            Table 3.2 shows that the four cues separate the five grammars: any two differ on some cue.

                                            The Norwegian children hear the cues for non-V2 in exclamatives and embedded questions.

                                            The rows #

                                            The cell a row's clause or wh feature records; an embedded question is Belfast's yes/no-question.

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                                              A row records the verb as moved, as in V2 and in the V1 of a yes/no-question, as unmoved, or as either.

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                                                def Westergaard2009.instReprOrder.repr :
                                                Order → ℕ → Std.Format
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                                                  The order a row's order feature records.

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                                                    The fragment of a row's variety, Standard Norwegian, Nordmøre, Standard or Belfast English or Danish; the Tromsø rows have none.

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                                                      An order is consistent with a distribution at a cell when a moved verb sits where verb second is possible, an unmoved one where it is not required, and either where it is optional.

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                                                        theorem Westergaard2009.rows_consistent (r : Datum) :
                                                        r ∈ Examples.all → r.feature? "adverb" = none → ∀ d ∈ grammarOf r, ∀ c ∈ cellOf r, ∀ o ∈ orderOf r, Order.Consistent d c o

                                                        Every judged word order in the data is consistent with the fragment of its variety, apart from the kanskje rows, which the chapter treats as a lexical exception.

                                                        Wh-heads and information structure (§3.2, §3.3) #

                                                        A wh-element is a head, sitting in Int⁰ itself, or a phrase in its specifier.

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                                                            A monosyllabic wh-word is a head, a longer one a phrase.

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                                                              A wh-head sits in Int⁰ itself and blocks verb movement to it in a root wh-question; a phrase in the specifier blocks nothing.

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                                                                The wh-elements of the Tromsø dialect.

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                                                                    The status of each wh-word, by its syllable count.

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                                                                      ka, kem and kor are heads and block verb movement to Int⁰; the others are phrases and block nothing.

                                                                      Which element checks the [−foc] feature of Top⁰ in a monosyllabic wh-question: a [−foc] subject from the specifier (32), otherwise the finite verb in the head (31).

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                                                                        def Westergaard2009.instReprChecker.repr :
                                                                        Checker → ℕ → Std.Format
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                                                                          The words whose order the two structures fix.

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                                                                            def Westergaard2009.instReprWord.repr :
                                                                            Word → ℕ → Std.Format
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                                                                              def Westergaard2009.order (subjectFoc : Focus.Mark) :
                                                                              List Word

                                                                              The surface order puts the wh-head in Int⁰, then the specifier and head of TopP, then the rest of the clause.

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                                                                                Verb second holds when the finite verb is the second word.

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                                                                                  theorem Westergaard2009.isV2_order_iff (subjectFoc : Focus.Mark) :
                                                                                  IsV2 (order subjectFoc) ↔ subjectFoc = Focus.Mark.focused

                                                                                  A monosyllabic wh-question is V2 exactly when its subject is new information.