Unidirectional Derivation Semantics for Synchronous Tree-Adjoining - PowerPoint PPT Presentation

Unidirectional Derivation Semantics for Synchronous Tree-Adjoining Grammars Matthias Büchse 1 and Andreas Maletti 2 and Heiko Vogler 1 1 Faculty of Computer Science 2 Institute for Natural Language Processing Technische Universität Dresden Universität Stuttgart 01062 Dresden, Germany 70569 Stuttgart, Germany maletti@ims.uni-stuttgart.de Taipei — August 17, 2012 Andreas Maletti DLT 2012 1

Tree-Adjoining Grammars Motivation [J OSHI ] • mildly context-sensitive formalism • local dependencies in rules Andreas Maletti DLT 2012 2

Tree-Adjoining Grammars Motivation [J OSHI ] • mildly context-sensitive formalism • local dependencies in rules • but global dependencies in derivation Andreas Maletti DLT 2012 3

Tree-Adjoining Grammars Motivation [J OSHI ] • mildly context-sensitive formalism • local dependencies in rules • but global dependencies in derivation Applications • TAG for English [XTAG G ROUP 2001] • TAG for German [K ALLMEYER et al. 2010] Andreas Maletti DLT 2012 4

Tree-Adjoining Grammars Definition (J OSHI et al. 1969) Tree-adjoining grammar (TAG) has a finite set of • substitution rules • adjunction rules Substitution rule (rules of a regular tree grammar): NP NP of NP Andreas Maletti DLT 2012 5

Tree-Adjoining Grammars S Andreas Maletti DLT 2012 6

Tree-Adjoining Grammars Used substitution rule S S NP VP NP VP Andreas Maletti DLT 2012 7

Tree-Adjoining Grammars Used substitution rule S NP NP VP N N children children Andreas Maletti DLT 2012 8

Tree-Adjoining Grammars Used substitution rule S VP NP VP V NP N V NP children Andreas Maletti DLT 2012 9

Tree-Adjoining Grammars Used substitution rule S V NP VP like N V NP children like Andreas Maletti DLT 2012 10

Tree-Adjoining Grammars Used substitution rule S NP NP VP N N V NP children like N Andreas Maletti DLT 2012 11

Tree-Adjoining Grammars Used substitution rule S N NP VP candies N V NP children like N candies Andreas Maletti DLT 2012 12

Tree-Adjoining Grammars Definition (J OSHI et al. 1969) Tree-adjoining grammar (TAG) has a finite set of • substitution rules • adjunction rules Adjunction rule: N ADJ � Andreas Maletti DLT 2012 13

Tree-Adjoining Grammars Used adjunction rule S N NP VP ADJ � N V NP children like N candies Andreas Maletti DLT 2012 14

Tree-Adjoining Grammars Used adjunction rule S N NP VP ADJ � N V NP children like N ADJ � N candies Andreas Maletti DLT 2012 15

Tree-Adjoining Grammars Used adjunction rule S N NP VP ADJ � N V NP children like N ADJ � N candies Andreas Maletti DLT 2012 16

Tree-Adjoining Grammars Used adjunction rule S N NP VP ADJ � N V NP children like N ADJ N candies Andreas Maletti DLT 2012 17

Tree-Adjoining Grammars Used adjunction rule S N NP VP ADJ � N V NP children like N Used substitution rule ADJ N ADJ red candies red Andreas Maletti DLT 2012 18

Synchronous Tree-Adjoining Grammars Definition (S HIEBER and S CHABES 1990) Synchronous tree-adjoining grammar (STAG) consists of two synchronized TAG Substitution rule: NP NP — NP of NP NP NP Andreas Maletti DLT 2012 19

Synchronous Tree-Adjoining Grammars Definition (S HIEBER and S CHABES 1990) Synchronous tree-adjoining grammar (STAG) consists of two synchronized TAG Adjunction rule: N N — ADJ ADJ � � Andreas Maletti DLT 2012 20

Synchronous Tree-Adjoining Grammars S S Andreas Maletti DLT 2012 21

Synchronous Tree-Adjoining Grammars S S NP VP NP VP Andreas Maletti DLT 2012 22

Synchronous Tree-Adjoining Grammars S S NP VP NP VP N DET N children les enfants Andreas Maletti DLT 2012 23

Synchronous Tree-Adjoining Grammars S S NP VP NP VP N V NP DET N V NP children les enfants Andreas Maletti DLT 2012 24

Synchronous Tree-Adjoining Grammars S S NP VP NP VP N V NP DET N V NP children like les enfants aiment Andreas Maletti DLT 2012 25

Synchronous Tree-Adjoining Grammars S S NP VP NP VP N V NP DET N V NP children like les aiment N enfants DET N les Andreas Maletti DLT 2012 26

Synchronous Tree-Adjoining Grammars S S NP VP NP VP N V NP DET N V NP children like les aiment N enfants DET N candies les bonbons Andreas Maletti DLT 2012 27

Synchronous Tree-Adjoining Grammars S S NP VP NP VP N V NP DET N V NP children like N les enfants aiment DET N ADJ N les N ADJ candies bonbons Andreas Maletti DLT 2012 28

Synchronous Tree-Adjoining Grammars S S NP VP NP VP N V NP DET N V NP children like N les enfants aiment DET N ADJ N les N ADJ rouges red candies bonbons Andreas Maletti DLT 2012 29

Contents Motivation 1 2 Synchronous Tree-Adjoining Grammars Relating STAG and XTOP 3 Bimorphism Semantics 4 Summary 5 Andreas Maletti DLT 2012 30

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 α x 2 α α α β t Andreas Maletti DLT 2012 31

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 x 1 x 2 α α α β t � α � 0 t 1 Andreas Maletti DLT 2012 32

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 α x 2 α α α β t � α � 0 t 1 Andreas Maletti DLT 2012 33

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 α x 2 α α α β t � α � 0 1 = t � x 1 /α � 0 t Andreas Maletti DLT 2012 34

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ x 1 x 2 α x 2 x 1 x 2 α α α t � α � 0 1 = t � x 1 /α � 0 t � γ ( � , β ) � 1 t 2 Andreas Maletti DLT 2012 35

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 α x 2 β � α α α t � α � 0 1 = t � x 1 /α � 0 t � γ ( � , β ) � 1 t 2 Andreas Maletti DLT 2012 36

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 α x 2 β � α α α t � α � 0 1 = t � x 1 /α � 0 t � γ ( � , β ) � 1 t 2 Andreas Maletti DLT 2012 37

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 α x 2 α α α β t � α � 0 1 = t � x 1 /α � 0 t � γ ( � , β ) � 1 t 2 Andreas Maletti DLT 2012 38

Tree Substitution Types • first-order : t � u � 0 v replaces leaf at v in t by u • second-order : t � u � 1 v replaces unary node at v in t by u (with the subtree at v 1 substituted into u ) σ σ σ γ x 1 x 1 x 2 α x 2 α α α β t � α � 0 1 = t � x 1 /α � 0 t � γ ( � , β ) � 1 2 = t � x 2 /γ ( � , β ) � 1 t Andreas Maletti DLT 2012 39

Monadic Doubly Ranked Alphabet Definition Alphabet Q with a mapping rk : Q → { 0 , 1 } 2 Andreas Maletti DLT 2012 40

Monadic Doubly Ranked Alphabet Definition Alphabet Q with a mapping rk : Q → { 0 , 1 } 2 Notes • input and output rank rk 1 and rk 2 • rank 0 → first-order substitution t � · · · � 0 • rank 1 → second-order substitution t � · · · � 1 Andreas Maletti DLT 2012 41

Monadic Doubly Ranked Alphabet Definition Alphabet Q with a mapping rk : Q → { 0 , 1 } 2 Notes • input and output rank rk 1 and rk 2 • rank 0 → first-order substitution t � · · · � 0 • rank 1 → second-order substitution t � · · · � 1 • Q ( i , j ) = { q ∈ Q | rk ( q ) = ( i , j ) } Andreas Maletti DLT 2012 42