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A performance theory of order and constituency

Hawkins, J. A. (1994). Cambridge University Press

The parser builds a phrasal mother as soon as it meets a word whose category determines it. A mother's constituent recognition domain runs from the word constructing its first immediate constituent to the word constructing its last, and Early Immediate Constituents prefers orders whose domains recognize the constituents in the fewest words. A domain read right to left keeps its words in reverse order, so the ratio of constituents to words cannot tell an order from its mirror image, while the left-to-right ratio can. Of a head over a phrase whose head has a complement, the consistent orders score best, and the head kept leftmost beats the phrase kept leftmost.

Implementation notes

A constituent enters a domain as the words before and after its constructing word (IC). Phrase-structure trees over PhraseStructure.Cat give these numbers through Mother Node Construction (toIC), with the constructing categories of p. 61; the schematic orders of (3.16), printed as category strings, enter as constituents directly.
Ratios are exact rationals; the book prints them as rounded percentages.
The ratio of constituents to non-terminal nodes is not formalized: the book uses the ratio to words as its shorthand (p. 75).

References

Hawkins 1994, A performance theory of order and constituency

Constituent recognition domains

A recognition domain read right to left contributes its words in reverse order.

theorem crd_mirror L119–129

(l : List IC) :

crd (mirror l) = (crd l).reverse

Built from , ,

L132–133

Mother Node Construction

The left-to-right ratio

L173–175

(3.16'): of three noun-phrase domains of six words with a four-word clause, the order with the single-word constituents first scores 83.3%, the clause between them 63.3%, and the clause first 38.3%.

theorem leftToRight_3_16 L177–183

leftToRight [{ pre := 0, post := 0 }, { pre := 0, post := 0 }, { pre := 3, post := 0 }] = 5 / 6 ∧ leftToRight [{ pre := 0, post := 0 }, { pre := 3, post := 0 }, { pre := 0, post := 0 }] = 19 / 30 ∧ leftToRight [{ pre := 0, post := 3 }, { pre := 0, post := 0 }, { pre := 0, post := 0 }] = 23 / 60

Built from

A head over a phrase, (3.22)

(3.22), pp. 96–97 and 254: when the lower head has a complement, the two consistent orders of a head over a phrase score 100%, the head kept leftmost [C IC] scores less, and the phrase kept leftmost [IC C] less still.

theorem leftToRight_binary_lt L219–234

{m : ℕ} (hm : 0 < m) (d : HeadDirection) :

leftToRight (binary HeadDirection.headFinal HeadDirection.headInitial m) < leftToRight (binary HeadDirection.headInitial HeadDirection.headFinal m) ∧ leftToRight (binary HeadDirection.headInitial HeadDirection.headFinal m) < leftToRight (binary d d m) ∧ leftToRight (binary d d m) = 1

Built from ,

(5.3) and (5.4)

L242–245

L247–250

(5.3'), (5.4'), p. 255: the domains of (5.3) and (5.4) are mirror images of each other; both recognize two constituents in four words, 50%, but read left to right (5.3) scores 75% and (5.4) 42%.

theorem ratios_5_3 L252–268

ics ex5_3 = some (binary HeadDirection.headInitial HeadDirection.headFinal 2) ∧ ics ex5_4 = some (mirror (binary HeadDirection.headInitial HeadDirection.headFinal 2)) ∧ icToWord (binary HeadDirection.headInitial HeadDirection.headFinal 2) = 1 / 2 ∧ icToWord (mirror (binary HeadDirection.headInitial HeadDirection.headFinal 2)) = 1 / 2 ∧ leftToRight (binary HeadDirection.headInitial HeadDirection.headFinal 2) = 3 / 4 ∧ leftToRight (mirror (binary HeadDirection.headInitial HeadDirection.headFinal 2)) = 5 / 12

Built from , , , , , ,