Dependency-length minimization and its limits: A possible role for a probabilistic version of the final-over-final condition

A two-dependency catena is a dependency with a dependency of its dependent (hierarchical) or two of one head (parallel), harmonic when both point one way. The paper scores a sentence by the chance that a baseline relinearization has longer catenae. Mirroring keeps harmony and the score and exchanges head-final with head-initial pairs, so a law invariant under it, such as one weighting length alone, gives the score one law at k head-final and at k head-initial pairs. A score falling with head-finality needs a cause that sees direction, such as a penalty on final over initial.

Implementation notes

• A sentence is a linearization σ of a tree g, the graph g.map σ: catenae and their head–dependent pairs are read off g, directions and lengths off σ. Only dependencies between verbs, nouns, adjectives and adverbs are measured, at distances counting every word; on catenae covering every arc the length is the total dependency length (length_eq_totalLength).
• dlm is the probability that the paper estimates from 100 baseline samples, for any baseline law; fig2a is one sample.
• The paper's tentative principle is modelled one catena at a time (disprefer): the final-over-initial configuration of a catena is downweighted by ε < 1 in a mirror-invariant law. Like the paper, the model drops both restrictions of Biberauer, Holmberg and Roberts, that the two heads lie in one extended projection and share their value of ±V.
• The symmetry argument is the one Roberts makes against harmony as the source of the condition, in his chapter of the book of Sheehan, Biberauer, Roberts and Holmberg, whose chapter by Sheehan weighs the parsing accounts of the condition.

Errata

• Fig. 2b, the free-word-order baseline, attaches into and certain to article, so it is not the dependency-preserving linearization of Figure 1 that §2.3 describes; with the heads of Figure 1 its order puts into after parts, reversing a dependency the baseline keeps.
• The reference list credits "Harmony, symmetry, and dominance in word order universals" to Biberauer, Holmberg, Roberts and Sheehan; the chapter is Roberts's alone.

TODO

• The paper's three baselines as laws on projective linearizations, which needs the supplementary materials on function words and the order of siblings. dlm_mirror and measure_dlm_headFinal hold for every baseline.
• A law downweighting every final-over-initial catena of a sentence does not reduce to the model of one catena, since the other catenae break the symmetry measure_swap_directions gives.
• Behaghel's law against nested ordering: the second is mirror-symmetric and the first is not.

References

• Jing et al. 2022, Dependency-length minimization and its limits: A possible role for a probabilistic version of the final-over-final condition
• Biberauer et al. 2014, A syntactic universal and its consequences
• Sheehan et al. 2017, The final-over-final condition: A syntactic universal
• Sheehan 2017b, The final-over-final condition and processing formalized