Kuhlmann 2013: Mildly Non-Projective Dependency Grammar

[Kuh13]

Figure 1's Dutch/German minimal pair — cross-serial dependencies against nested infinitives, the same dependencies in opposite verb-cluster orders — and the LCFRS coverage data of Tables 3-4: rule and tree loss under fan-out and well-nestedness bounds for five languages from the CoNLL 2006 shared task.

Main declarations

• Kuhlmann2013.dutchCrossSerial, Kuhlmann2013.germanNested: Figure 1's minimal pair, separated by gap degree
• 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

Figure 1: cross-serial against nested

The same dependencies in opposite verb-cluster orders. The Dutch order is non-projective and the German one is not, so the pair separates the two regimes while holding the dependency structure fixed.

def Kuhlmann2013.dutchCrossSerial : DependencyGrammar.Graph 7

Dutch cross-serial: "dat Jan Piet Marie zag helpen lezen".

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

def Kuhlmann2013.germanNested : DependencyGrammar.Graph 7

German nested: "dass Jan Piet Marie lesen helfen sah".

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

def Kuhlmann2013.dutchTree : DependencyGrammar.Tree 7

The Dutch fixture as a bundled Tree: the dominance-order API applies with no side conditions.

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• Kuhlmann2013.dutchTree = DependencyGrammar.Tree.mk' Kuhlmann2013.dutchCrossSerial Kuhlmann2013.dutchTree._proof_1

Tables 3-4: LCFRS coverage

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 : ℕ
• totalTrees : ℕ
• rulesLostFanout1 : ℕ

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

• treesLostFanout1 : ℕ

  Trees lost at fan-out = 1

• rulesLostFanout2 : ℕ

  Rules lost at fan-out ≤ 2

• treesLostFanout2 : ℕ

  Trees lost at fan-out ≤ 2

• rulesLostWN : ℕ

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

• treesLostWN : ℕ

  Trees lost when also requiring well-nestedness

@[instance_reducible]

instance Kuhlmann2013.instReprLCFRSCoverage : Repr LCFRSCoverage

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

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

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def Kuhlmann2013.arabic : LCFRSCoverage

Arabic row of [Kuh13] Tables 3-4.

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def Kuhlmann2013.czech : LCFRSCoverage

Czech row of [Kuh13] Tables 3-4.

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def Kuhlmann2013.danish : LCFRSCoverage

Danish row of [Kuh13] Tables 3-4.

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

def Kuhlmann2013.slovene : LCFRSCoverage

Slovene row of [Kuh13] Tables 3-4.

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def Kuhlmann2013.turkish : LCFRSCoverage

Turkish row of [Kuh13] Tables 3-4.

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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).