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論文紹介:Learning Dependency-Based Compositional Se...

yuri
October 11, 2021

論文紹介:Learning Dependency-Based Compositional Semantics

yuri

October 11, 2021
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  1. • 論理形式zにはどんな形式⾔語を⽤いるのが良いか︖ • SQL (Giordani and Moschitti 2009) • Prolog

    (Zelle and Mooney 1996; Tang and Mooney 2001) • FunQL (Kate, Wong, and Mooney 2005) • Lambda calculus (Zettlemoyer and Collins 2005) • 論理形式の構成にはどんな⽣成規則を⽤いるのが良いか︖ • Synchronous grammars (Wong and Mooney 2007) • Hybrid trees (Lu et al. 2008) • Combinatory Categorial Grammars (CCG) (Zettlemoyer and Collins 2005) • Shift-reduce derivations (Zelle and Mooney 1996) • これらとは異なる形式⾔語と⽣成規則を持つDependency-based compositional semantics (DCS) を考案 Semantic representation 3 DCS tree
  2. DCS のsyntaxは predicate と relation から構成︓ predicate • a special

    null predicate ø • domain-independent predicates (e.g., count, <, >, and =) • domain-specific predicates (e.g., state, river, border, etc.) relation • Table 1 を参照 Syntax 4
  3. • DCSにおける論理形式を DCS treeという • DCS tree は directed rooted

    tree • ノードには predicate、エッジにはrelationをラベル付け • 各ノードは⼦に対して順序を保つ Syntax 5 Definition 1 (DCS trees)
  4. • データベースのことを worldと呼ぶ • まず、valueの集合 Vを作成 • number (e.g., 3

    ∈ V) • string (e.g., Washington ∈ V) • tuple (e.g., (3, Washington) ∈ V) • set (e.g., {3, Washington} ∈ V) • other higher-order entities • world は各predicate をそのsemantics, つまり組の集合に写像 • 𝑉{TUPLE}はすべての組の集合を表す︓ World 6 Definition 2 (World)
  5. • world wに対するDCS tree z のsemantics または denotation を 𝑧

    ! と表す • syntaxとsemanticsのスコープの違い (e.g., generalized quantification, superlative constructions) を統⼀的に扱うために mark-executeを導⼊ Semantics 8
  6. Quantifier scope ambiguity 9 e.g., Some river traverses every city.

    The two meanings are: (i) There is a river x such that x traverses every city. (ii) For every city x, some river traverses x.
  7. Superlative scope ambiguity 10 e.g., state bordering the largest state

    The two meanings are: (i) a state that borders Alaska (which is the largest state) (ii) a state with the highest score, where the score of a state x is the maximum size of any state that x borders (Alaska is irrelevant here because no states border it)
  8. • denotation d にはn個の columnが含まれる • column 1は常にroot nodeに対応 •

    残りのcolumnはnon-root marked nodeに対応 • non-marked nodeについては量化するので対応するcolumnはない • denotation d は配列の集合 d.Aと、marked nodeごとにそれが実⾏される ときに引き出される情報を格納した store σを持つ Denotation 11 • mark relation σ.r (C) • base denotation σ.b, which essentially corresponds to denotation of the subtree rooted at the marked node excluding the mark relation and its subtree ( 𝑠𝑖𝑧𝑒 ! ) • mark relationの⼦のdenotation ( 𝑎𝑟𝑔𝑚𝑎𝑥 ! ) • markされていない nodeのstoreは常に 空 (σ=ø)
  9. 先にproject operationを定義︓ øをnon-initial columns with empty stores (i>1 such that

    𝑑. 𝜎! = 𝜙)のindexを表すのにも使⽤ join-project-inactive operation は2つのdenotationの配列を結合し、non-initial empty columnを消去 • join はcolumn 1に作⽤ • ∗ はすべての要素を表す、つまり ⋈∗,∗ $% は組全体が⼀致しなければならないという結合条 件を⽰す (𝑎& = 𝑎& ' ) Join 14
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