Kuhlmann 2013: Mildly Non-Projective Dependency Grammar

[Kuh13]

LCFRS coverage data from [Kuh13] Tables 3-4 (Computational Linguistics 39(2)): rule and tree loss under fan-out and well-nestedness bounds for five languages from the CoNLL 2006 shared task.

Main declarations

• Kuhlmann2013.LCFRSCoverage: rule/tree loss row under fan-out bounds
• Kuhlmann2013.arabic, Kuhlmann2013.czech, Kuhlmann2013.danish, Kuhlmann2013.slovene, Kuhlmann2013.turkish: Tables 3-4 rows
• Kuhlmann2013.fanout2_good_coverage: fan-out ≤ 2 loses under 1% of trees in every language

structure Kuhlmann2013.LCFRSCoverage : Type

[Kuh13] Table 3: rule/tree loss under fan-out bounds. Five languages from the CoNLL 2006 shared task.

• name : String
• totalRules : Nat
• totalTrees : Nat
• rulesLostFanout1 : Nat

  Rules lost at fan-out = 1 (projective only)

• treesLostFanout1 : Nat

  Trees lost at fan-out = 1

• rulesLostFanout2 : Nat

  Rules lost at fan-out ≤ 2

• treesLostFanout2 : Nat

  Trees lost at fan-out ≤ 2

• rulesLostWN : Nat

  Rules lost when also requiring well-nestedness (with fan-out ≤ 2)

• treesLostWN : Nat

  Trees lost when also requiring well-nestedness

@[implicit_reducible]

instance Kuhlmann2013.instReprLCFRSCoverage : Repr LCFRSCoverage

Equations

• Kuhlmann2013.instReprLCFRSCoverage = { reprPrec := Kuhlmann2013.instReprLCFRSCoverage.repr }

def Kuhlmann2013.instReprLCFRSCoverage.repr : LCFRSCoverage → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def Kuhlmann2013.arabic : LCFRSCoverage

Arabic row of [Kuh13] Tables 3-4.

Equations

• One or more equations did not get rendered due to their size.

def Kuhlmann2013.czech : LCFRSCoverage

Czech row of [Kuh13] Tables 3-4.

Equations

• One or more equations did not get rendered due to their size.

def Kuhlmann2013.danish : LCFRSCoverage

Danish row of [Kuh13] Tables 3-4.

Equations

• One or more equations did not get rendered due to their size.

def Kuhlmann2013.slovene : LCFRSCoverage

Slovene row of [Kuh13] Tables 3-4.

Equations

• One or more equations did not get rendered due to their size.

def Kuhlmann2013.turkish : LCFRSCoverage

Turkish row of [Kuh13] Tables 3-4.

Equations

• One or more equations did not get rendered due to their size.

theorem Kuhlmann2013.fanout2_good_coverage : arabic.treesLostFanout2 ≤ 1 ∧ czech.treesLostFanout2 * 100 / czech.totalTrees < 1 ∧ danish.treesLostFanout2 * 100 / danish.totalTrees < 1 ∧ slovene.treesLostFanout2 * 100 / slovene.totalTrees < 1 ∧ turkish.treesLostFanout2 * 100 / turkish.totalTrees < 1

Fan-out ≤ 2 (block-degree ≤ 2) loses very few trees across all languages ([Kuh13] Tables 3-4).