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 #
V2Grammar: a set of cells, the clause-type heads the finite verb moves to.stdNorwegian,stdEnglish,nordmore,belfast,german,danish: the grammars of Table 3.1.MicroCue,Expresses: a cue and its expression by a grammar.TromsøWh,WhStatus,order: the Tromsø wh-words, their status, and the word order of a monosyllabic wh-question.
Main results #
table_3_1_eq_required,danish_table_3_1: Table 3.1 against the fragments.nordmore_english_mirror,embedded_german_polar_all: the mirror image and the two universals read off the fragments.table_3_2,not_expresses_both: the four cues separate the five grammars.rows_consistent: every judged word order in the data is consistent with its fragment.isV2_order_iff: a Tromsø monosyllabic wh-question is verb second iff its subject is new.
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 #
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) #
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.
Nordmøre Norwegian is the mirror image of Standard English on Decl⁰ and Int⁰.
Only German requires verb second in an embedded declarative, and every variety requires it in a root yes/no-question.
Micro-cues (§4) #
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- Westergaard2009.instDecidableEqFiller x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Westergaard2009.instReprFiller = { reprPrec := Westergaard2009.instReprFiller.repr }
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A micro-cue: for one cell, what its specifier holds and whether the finite verb fills its head.
- target : Clause.SentenceType × Clause.EmbeddingContext
- spec : Filler
- verbInHead : Bool
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- Westergaard2009.instReprMicroCue = { reprPrec := Westergaard2009.instReprMicroCue.repr }
The cue (45) is V2 in wh-questions.
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- Westergaard2009.cueIntV2 = { target := Clause.root Clause.SentenceType.constituent, spec := Westergaard2009.Filler.wh, verbInHead := true }
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The cue (46) is V2 in declaratives.
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- Westergaard2009.cueDeclV2 = { target := Clause.root Clause.SentenceType.declarative, spec := Westergaard2009.Filler.xp, verbInHead := true }
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The cue (49) is V2 in yes/no-questions.
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- Westergaard2009.cuePolV2 = { target := Clause.root Clause.SentenceType.polar, spec := Westergaard2009.Filler.none, verbInHead := true }
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The cue (52) is V2 in exclamatives.
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- Westergaard2009.cueExclV2 = { target := Clause.root Clause.SentenceType.exclamative, spec := Westergaard2009.Filler.wh, verbInHead := true }
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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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- Westergaard2009.cueWhV2 = { target := (Clause.SentenceType.polar, Clause.EmbeddingContext.quasiSubordinated), spec := Westergaard2009.Filler.wh, verbInHead := true }
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The cue (54) is V2 in imperatives.
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- Westergaard2009.cueImpV2 = { target := Clause.root Clause.SentenceType.imperative, spec := Westergaard2009.Filler.none, verbInHead := true }
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The cue (58) is non-V2 in exclamatives.
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- Westergaard2009.cueExclNonV2 = { target := Clause.root Clause.SentenceType.exclamative, spec := Westergaard2009.Filler.wh, verbInHead := false }
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The cue (59) is non-V2 in embedded questions.
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- Westergaard2009.cueWhNonV2 = { target := (Clause.SentenceType.polar, Clause.EmbeddingContext.quasiSubordinated), spec := Westergaard2009.Filler.wh, verbInHead := false }
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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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- Westergaard2009.Expresses lang c = (c.target ∈ lang ↔ c.verbInHead = true)
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- Westergaard2009.instDecidableExpressesOfMemProdSentenceTypeEmbeddingContextV2GrammarTarget lang c = { decide := decide (c.target ∈ lang) == decide (c.verbInHead = true), reflects_decide := ⋯ }
A cue and the cue for its absence are never both expressed.
The four cues of Table 3.2.
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The five grammars of Table 3.2.
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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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- Westergaard2009.instDecidableEqOrder x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Westergaard2009.instReprOrder = { reprPrec := Westergaard2009.instReprOrder.repr }
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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- Westergaard2009.Order.Consistent d c Westergaard2009.Order.moved = (c ∈ d.possible)
- Westergaard2009.Order.Consistent d c Westergaard2009.Order.unmoved = (c ∉ d.required)
- Westergaard2009.Order.Consistent d c Westergaard2009.Order.either = (c ∈ d.possible ∧ c ∉ d.required)
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- Westergaard2009.instDecidablePredOrderConsistent d c Westergaard2009.Order.unmoved = { decide := !decide (c ∈ d.required), reflects_decide := ⋯ }
- Westergaard2009.instDecidablePredOrderConsistent d c Westergaard2009.Order.either = { decide := decide (c ∈ d.possible) && decide (c ∉ d.required), reflects_decide := ⋯ }
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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- Westergaard2009.instDecidableEqWhStatus x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Westergaard2009.instReprWhStatus = { reprPrec := Westergaard2009.instReprWhStatus.repr }
A monosyllabic wh-word is a head, a longer one a phrase.
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- Westergaard2009.WhStatus.ofSyllables n = if n ≤ 1 then Westergaard2009.WhStatus.head else Westergaard2009.WhStatus.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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- w.Blocks c = (w = Westergaard2009.WhStatus.head ∧ c = Clause.root Clause.SentenceType.constituent)
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- Westergaard2009.instDecidableEqTromsøWh x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Westergaard2009.instReprTromsøWh = { reprPrec := Westergaard2009.instReprTromsøWh.repr }
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Their syllable counts.
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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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- Westergaard2009.instDecidableEqChecker x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Westergaard2009.instReprChecker = { reprPrec := Westergaard2009.instReprChecker.repr }
The checker, by the focus marking of the subject.
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- Westergaard2009.instDecidableEqWord x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Westergaard2009.instReprWord.repr Westergaard2009.Word.wh prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Westergaard2009.Word.wh")).group prec✝
- Westergaard2009.instReprWord.repr Westergaard2009.Word.verb prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Westergaard2009.Word.verb")).group prec✝
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- Westergaard2009.instReprWord = { reprPrec := Westergaard2009.instReprWord.repr }
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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- Westergaard2009.IsV2 l = (l[1]? = some Westergaard2009.Word.verb)
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A monosyllabic wh-question is V2 exactly when its subject is new information.