Treebank Non-Projectivity Constraints

@cite{kuhlmann-nivre-2006} @cite{kuhlmann-2013}

Connects the structural theory of non-projectivity to empirical treebank data on the prevalence of well-nestedness, gap degree, and fan-out constraints.

Key Results

• Well-nestedness covers ≥99% of both PDT and DDT (@cite{kuhlmann-nivre-2006} Table 1)
• Gap degree ≤ 1 covers ≥99% of both treebanks
• Planarity is insufficient (covers far less than well-nestedness)
• Fan-out ≤ 2 (block-degree ≤ 2) loses very few trees across all languages

theorem Phenomena.WordOrder.Studies.KuhlmannNivre2006.wellNested_near_universal : NonProjectivity.pdt.wellNested ≥ 9900 ∧ NonProjectivity.ddt.wellNested ≥ 9900

Well-nestedness covers ≥99% of both treebanks (@cite{kuhlmann-nivre-2006} Table 1).

theorem Phenomena.WordOrder.Studies.KuhlmannNivre2006.gapDeg_leq1_sufficient : NonProjectivity.pdt.gapDeg0 + NonProjectivity.pdt.gapDeg1 ≥ 9900 ∧ NonProjectivity.ddt.gapDeg0 + NonProjectivity.ddt.gapDeg1 ≥ 9900

Gap degree ≤ 1 covers ≥99% of both treebanks.

theorem Phenomena.WordOrder.Studies.KuhlmannNivre2006.planarity_insufficient : NonProjectivity.pdt.planar < NonProjectivity.pdt.wellNested ∧ NonProjectivity.ddt.planar < NonProjectivity.ddt.wellNested

Planarity covers far less than well-nestedness.

theorem Phenomena.WordOrder.Studies.KuhlmannNivre2006.fanout2_good_coverage : NonProjectivity.arabic.treesLostFanout2 ≤ 1 ∧ NonProjectivity.czech.treesLostFanout2 * 100 / NonProjectivity.czech.totalTrees < 1 ∧ NonProjectivity.danish.treesLostFanout2 * 100 / NonProjectivity.danish.totalTrees < 1 ∧ NonProjectivity.slovene.treesLostFanout2 * 100 / NonProjectivity.slovene.totalTrees < 1 ∧ NonProjectivity.turkish.treesLostFanout2 * 100 / NonProjectivity.turkish.totalTrees < 1

Fan-out ≤ 2 (block-degree ≤ 2) loses very few trees across all languages (@cite{kuhlmann-2013} Tables 3-4).