Fedzechkina, Chu and Jaeger (2018): Human information processing shapes language change #
Fedzechkina, Chu and Jaeger taught English speakers two miniature languages with free order of subject and object, one verb-final and one verb-initial, from input in which both orders were equally frequent and the two arguments always equally long. Describing scenes with one long argument, verb-final learners put it first and verb-initial learners put it last, the orders that shorten the verb's dependencies, although English prefers short before long (Arnold, Wasow, Losongco and Ginstrom); their productions had shorter dependencies than the input.
The paper measures the verb's dependency length as the summed distance in words from the verb to
the closest boundary of each argument: on its sentences, the yield distance of dependency graphs
(Graph.yieldDist), and on arrangements of subject, object and verb, the boundary distance of
constituents of given lengths (Arrangement.boundaryDist), which agree on Fig. 1 as the
substrate's bridge theorem predicts. The measure is invariant under mirroring, and with the verb
at an edge it is two plus the length of the argument next to the verb. A learner's productions
are a probability measure on pairs of the scene's long argument and the order used. Their mean
dependency length is affine in the probability of the symmetric difference of "the subject is
long" and "the subject comes first", which places every learner in the diamond of Fig. 5 and ties
Fig. 5 to the order proportions of Fig. 4.
Main statements #
verbDependencyLength_eq: the measure on a clause with the verb at an edge.integral_dependencyLength_eq_cond: the mean dependency length of a verb-final learner is an affine function of the difference of the subject-first proportions on the two kinds of scene.abs_integral_dependencyLength_sub_le: the diamond of Fig. 5.integral_dependencyLength_eq_lower_iff: who reaches its lower lines.
Implementation notes #
- A short argument is a bare noun, a long one a noun with an adpositional phrase of
L - 1words;L = 4in Figs. 1 and 2 and in every number of Fig. 5. - The measure of Fig. 5 is over the test productions with one long argument, the long subject
and the long object equally often (
P.fst = uniformOn {.subject, .object}); the short-short baseline is excluded, as in the paper. - Verb-final learners also used object-first order more often overall, which the paper ascribes to the bias to place the case-marked argument first seen in the authors' earlier experiments; the overall frequency is a free parameter here.
References #
The paper's measure #
The verb's dependency length sums the distances from the verb to the closest boundary of each argument (Fig. 1).
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- One or more equations did not get rendered due to their size.
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language d holds the orders of the miniature language whose verb has direction d
towards both arguments.
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The verb-initial orders are the mirror images of the verb-final ones; mirroring reverses the
order of subject and object (Arrangement.precedes_mirror).
With the verb at an edge, the measure is two plus the length of the argument in the middle, next to the verb.
In the verb-final language of Fig. 1, subject-first order is shorter exactly when the subject is the longer argument, long before short.
In the verb-initial language of Fig. 1, subject-first order is shorter exactly when the subject is the shorter argument, short before long.
With arguments of equal length the measure makes no ordering prediction (the baseline of Fig. 4).
Fig. 1 #
Fig. 1's verb-final sentence with subject first, MOUNTIE [[RED STOOL ON] HUNTER-OBJ] PUNCH, with the arcs of its bracketing.
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- One or more equations did not get rendered due to their size.
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Object first, [[RED STOOL ON] HUNTER-OBJ] MOUNTIE PUNCH.
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The verb-initial sentence with subject first, PUNCH MOUNTIE [HUNTER-OBJ [ON RED STOOL]].
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Object first, PUNCH [HUNTER-OBJ [ON RED STOOL]] MOUNTIE.
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The eight arrows of Fig. 1 are the yield distances from the verb, and they are the arrangement's boundary distances with the yields' lengths, the object four words long.
The printed numbers are 5 and 1, 1 and 2, 1 and 2, and 5 and 1.
The object's yield has four words and the subject's one.
Two events and their symmetric difference #
An event of probability one half differs from B with probability within
min (P B) (1 - P B) of one half.
Learners' productions #
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A test production pairs the long argument of the scene with the order used.
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A production is subject-first when the subject precedes the object.
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A production is in long c when c is the long argument of its scene.
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- FedzechkinaChuJaeger2018.long c = Prod.fst ⁻¹' {c}
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With the verb at an edge, an argument is next to it exactly when it stands in the middle.
dependencyLength L x is the verb's dependency length in the production x when its long
argument has L words and its other argument is a bare noun.
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- FedzechkinaChuJaeger2018.dependencyLength L x = ↑(FedzechkinaChuJaeger2018.verbDependencyLength x.2 (Function.update 1 x.1 L))
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In the verb-final language the long argument is next to the verb exactly when either the subject is long or it comes first, but not both.
The mean dependency length is three plus L - 1 times the probability that the long
argument is next to the verb.
Without a length-based ordering preference the mean is (L + 5) / 2, the input's 4.5, at
any overall order frequency, which is the dashed line of Fig. 5.
In the diamond of Fig. 5 the mean lies within L - 1 times the frequency of the rarer order of
the input's (L + 5) / 2.
The least mean length, 3, needs perfectly flexible order.
Fixed order gives the input's mean length.
The overall subject-first proportion averages those on the two kinds of scene.
A verb-final learner's mean dependency length is the input's minus (L - 1) / 2 times how
much more often they put the subject first when it is long than when the object is (Fig. 4), so
the paper's two analyses measure one quantity.
The lower lines of Fig. 5 are reached exactly by the verb-final learners who never put the subject first with a long object or always do with a long subject, spending subject-first order first where it shortens the dependencies; fixed order does so trivially.
Every point of the lower lines of Fig. 5 is reached, at subject-first frequency p by a
verb-final learner who spends subject-first order on long-subject scenes first.