A Tree Transducer Model for Synchronous Tree-Adjoining Grammars Andreas Maletti Universitat Rovira i Virgili Tarragona, Spain andreas.maletti@urv.cat Uppsala, Sweden — July 13, 2010 A Tree Transducer Model for STAG A. Maletti 1 ·
Synchronous Tree Substitution Grammar S S A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar S S CONJ S wa Used rule S — S CONJ S wa A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar S S CONJ S NP 1 VP NP 1 NP 2 wa V NP 2 V Used rule S S — NP VP V NP NP V NP A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar S S CONJ S NP 1 VP NP 1 NP 2 wa V NP 2 V ra’aa saw Used rule V V — saw ra’aa A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar S S NP VP CONJ S wa DT N V NP V NP NP saw the ra’aa N Used rule NP NP — DT N N the A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar S S NP VP CONJ S wa DT N V NP V NP NP boy saw ra’aa the N atefl Used rule N N — boy atefl A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar S S NP VP CONJ S DT N V NP wa V NP NP boy saw the DT N ra’aa N N the atefl Used rule NP NP — DT N N the A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar S S NP VP CONJ S DT N V NP wa V NP NP boy saw the DT N ra’aa N N atefl albab the door Used rule N N — door albab A Tree Transducer Model for STAG A. Maletti 2 ·
Synchronous Tree Substitution Grammar (cont’d) Advantages simple and natural model easy to train (from linguistic resources) symmetric Implementation extended top-down tree transducer in T IBURON [M AY , K NIGHT ’06] A Tree Transducer Model for STAG A. Maletti 3 ·
Synchronous Tree Substitution Grammar (cont’d) Synchronous tree substitution grammar rule: S S NP 1 VP w — NP 1 NP 2 V NP 2 V Corresponding extended top-down tree transducer rule: q S S S w q V q NP q NP − → x 1 VP x 2 x 1 x 3 x 2 x 3 A Tree Transducer Model for STAG A. Maletti 4 ·
Synchronous Tree-Adjoining Grammar S S A Tree Transducer Model for STAG A. Maletti 5 ·
Synchronous Tree-Adjoining Grammar S S NP VP NP VP Used substitution rule S S — NP VP NP VP A Tree Transducer Model for STAG A. Maletti 5 ·
Synchronous Tree-Adjoining Grammar S S NP 1 NP 1 VP VP NP 2 NP 2 V V Used substitution rule VP VP — V NP V NP A Tree Transducer Model for STAG A. Maletti 5 ·
Synchronous Tree-Adjoining Grammar S S NP 1 NP 1 VP VP NP 2 NP 2 V V likes aime Used substitution rule V V — likes aime A Tree Transducer Model for STAG A. Maletti 5 ·
Synchronous Tree-Adjoining Grammar S S NP VP NP VP V NP V NP likes N aime DT N les Used substitution rule NP NP — DT N N les A Tree Transducer Model for STAG A. Maletti 5 ·
Synchronous Tree-Adjoining Grammar S S NP VP NP VP V NP V NP likes N aime DT N candies les bonbons Used substitution rule N N — candies bonbons A Tree Transducer Model for STAG A. Maletti 5 ·
Synchronous Tree-Adjoining Grammar S S NP VP NP VP V NP V NP likes N aime DT N ADJ N les N ADJ candies bonbons Used adjunction rule N N — N ⋆ N ⋆ ADJ ADJ A Tree Transducer Model for STAG A. Maletti 5 ·
Synchronous Tree-Adjoining Grammar S S NP VP NP VP V NP V NP likes N aime DT N ADJ les ADJ N N rouges red candies bonbons Used substitution rule ADJ ADJ — rouges red A Tree Transducer Model for STAG A. Maletti 5 ·
Main Question Theorem Every STSG is an STAG. Question Are they further related? A Tree Transducer Model for STAG A. Maletti 6 ·
Roadmap Motivation 1 Explicit Substitution 2 3 Synchronous Tree-Adjoining Grammar Main Result 4 Application 5 A Tree Transducer Model for STAG A. Maletti 7 ·
First-Order Substitution Definition t [ v 1 ← t 1 , . . . , v k ← t k ] denotes the result obtained by replacing (in parallel) all occurrences of leaves labelled v i in t by t i . Example S S NP NP VP NP VP DT N DT N V NP V NP saw the the DT N saw the u t [ NP ← u ] t A Tree Transducer Model for STAG A. Maletti 8 ·
Second-Order Substitution Example · [ NP ← · ] S NP NP VP DT N V NP the saw Explicit substitution keep an explicit representation of substitutions in tree any number of substitutions allowed at any level A Tree Transducer Model for STAG A. Maletti 9 ·
Second-Order Substitution Example · [ NP ← · ] S NP NP VP DT N V NP the saw Evaluation eval ( · [ x ← · ]( t , u )) = eval ( t )[ x ← eval ( u )] eval ( σ ( t 1 , . . . , t k )) = σ ( eval ( t 1 ) , . . . , eval ( t k )) A Tree Transducer Model for STAG A. Maletti 9 ·
Second-Order Substitution Example Evaluation · [ NP ← · ] S NP VP S NP DT N V NP NP VP DT N saw the DT N V NP the the saw Evaluation eval ( · [ x ← · ]( t , u )) = eval ( t )[ x ← eval ( u )] eval ( σ ( t 1 , . . . , t k )) = σ ( eval ( t 1 ) , . . . , eval ( t k )) A Tree Transducer Model for STAG A. Maletti 9 ·
Roadmap Motivation 1 Explicit Substitution 2 3 Synchronous Tree-Adjoining Grammar Main Result 4 Application 5 A Tree Transducer Model for STAG A. Maletti 10 ·
Tree-Adjoining Grammar Intuition A TAG has two types of rules: substitution rules (as in TSG) adjunction rules Example (Adjunction) NP N NP DT N N ⋆ DT N ADJ les N ADJ rouges les bonbons rouges bonbons auxiliary derived adjunction tree tree A Tree Transducer Model for STAG A. Maletti 11 ·
Tree-Adjoining Grammar (cont’d) Simplifications (see [S HIEBER ’06]) no substitution rules adjunction mandatory (if possible) each adjunction spot used at most once root nodes of auxiliary trees are never adjunction spots Definition A TAG is a finite set of derived trees (initial trees) and auxiliary trees (those containing a starred node) A Tree Transducer Model for STAG A. Maletti 12 ·
Tree-Adjoining Grammar (cont’d) Simplifications (see [S HIEBER ’06]) no substitution rules adjunction mandatory (if possible) each adjunction spot used at most once root nodes of auxiliary trees are never adjunction spots Definition A TAG is a finite set of derived trees (initial trees) and auxiliary trees (those containing a starred node) A Tree Transducer Model for STAG A. Maletti 12 ·
Tree-Adjoining Grammar (cont’d) Example Derivation S S S S a S a S a S S T b S c S ⋆ a S a S b S S ⇒ a ⇒ b ⇒ auxiliary initial T S S tree S b tree c a T S a S S c T S T b S c S ⋆ c S ⋆ b String language auxiliary auxiliary tree tree { wcw | w ∈ { a , b } ∗ } A Tree Transducer Model for STAG A. Maletti 13 ·
Synchronous Tree-Adjoining Grammar Example S S S S — — a S S T T c c a S ⋆ a S ⋆ a initial tree pair auxiliary tree pair S S S S — — S b S S ⋆ S ⋆ S ⋆ S ⋆ b b b auxiliary tree pair auxiliary tree pair A Tree Transducer Model for STAG A. Maletti 14 ·
Synchronous Tree-Adjoining Grammar (cont’d) Example S S a S S S S S S S a S S b S — a — b — T T a a b b S S S S c c T T a a a S S c c T T c c String translation { ( wcw R , wcw ) | w ∈ { a , b } ∗ } A Tree Transducer Model for STAG A. Maletti 15 ·
Roadmap Motivation 1 Explicit Substitution 2 3 Synchronous Tree-Adjoining Grammar Main Result 4 Application 5 A Tree Transducer Model for STAG A. Maletti 16 ·
Simulation Question Can we simulate an STAG by some STSG? A Tree Transducer Model for STAG A. Maletti 17 ·
Simulation of Adjunction Example (TAG) Correspondence (TSG) S S · [ S ⋆ ← · ] S a · [ S ⋆ ← · ] a S T S S c S ⋆ a S S T auxiliary initial c a S ⋆ tree tree S S · [ S ⋆ ← · ] b S S b S S ⋆ S ⋆ S S S ⋆ b S ⋆ b auxiliary auxiliary tree tree A Tree Transducer Model for STAG A. Maletti 18 ·
Simulation of Adjunction (cont’d) Example · [ S ⋆ ← · ] · [ S ⋆ ← · ] · [ S ⋆ ← · ] · [ S ⋆ ← · ] S S S S S S S S a · [ S ⋆ ← · ] a · [ S ⋆ ← · ] a · [ S ⋆ ← · ] T T T T c ⇒ c ⇒ c ⇒ S S S S c S S · [ S ⋆ ← · ] S ⋆ a · [ S ⋆ ← · ] S ⋆ a b b S ⋆ a S S S S S ⋆ S ⋆ b S ⋆ b A Tree Transducer Model for STAG A. Maletti 19 ·
Simulation of Adjunction (cont’d) TSG result Evaluation · [ S ⋆ ← · ] · [ S ⋆ ← · ] S S S S a · [ S ⋆ ← · ] T a · [ S ⋆ ← · ] T c S S c S S · [ S ⋆ ← · ] S ⋆ a b b S S ⋆ a S S S S ⋆ S ⋆ b S ⋆ b Note coincides with the result obtained by TAG A Tree Transducer Model for STAG A. Maletti 20 ·
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