Strong Lexicalization of Tree-Adjoining Grammars Andreas Maletti 1 - PowerPoint PPT Presentation

Strong Lexicalization of Tree-Adjoining Grammars Andreas Maletti 1 and Joost Engelfriet 2 1 IMS, Universität Stuttgart, Germany 2 LIACS, Leiden University, The Netherlands maletti@ims.uni-stuttgart.de Stuttgart — May 2, 2012 Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 1 ·

Motivation Tree-Adjoining Grammars Motivation mildly context-sensitive formalism productions express local dependencies but can realize global dependencies Applications TAG for English [XTAG R ESEARCH G ROUP 2001] lexicalized TAG for German [K ALLMEYER et al. 2010] Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 2 ·

Motivation Tree-Adjoining Grammars Motivation mildly context-sensitive formalism productions express local dependencies but can realize global dependencies Applications TAG for English [XTAG R ESEARCH G ROUP 2001] lexicalized TAG for German [K ALLMEYER et al. 2010] Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 2 ·

Motivation Tree-Adjoining Grammars Motivation mildly context-sensitive formalism productions express local dependencies but can realize global dependencies Applications TAG for English [XTAG R ESEARCH G ROUP 2001] lexicalized TAG for German [K ALLMEYER et al. 2010] Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 2 ·

Motivation TAG — Syntax Definition (J OSHI et al. 1969) G = ( N , Σ , S , R ) tree-adjoining grammar (TAG) with finite set R substitution rules adjunction rules Example (Substitution rule) NP Σ NP of NP Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 3 ·

Motivation TAG — Syntax Definition (J OSHI et al. 1969) G = ( N , Σ , S , R ) tree-adjoining grammar (TAG) with finite set R substitution rules adjunction rules Example (Substitution rule) Example (Adjunction rule) N NP Σ Σ N ⋆ NP of NP ADJ Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 3 ·

Motivation TAG — Example Derivation S Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Example Derivation Used substitution rule S S NP VP NP VP Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Example Derivation Used substitution rule S VP NP 1 VP V NP NP 2 V Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Example Derivation Used substitution rule S V NP 1 VP likes NP 2 V likes Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Example Derivation Used substitution rule S NP NP VP N V NP likes N Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Example Derivation Used substitution rule S N NP VP candies V NP likes N candies Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Example Derivation Used adjunction rule S N NP VP N ⋆ ADJ V NP likes N ADJ N candies Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Example Derivation Used substitution rule S ADJ NP VP red V NP likes N ADJ N red candies Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 4 ·

Motivation TAG — Semantics Definition (Generated language) L ( G ) = { t ∈ T Σ | S ⇒ ∗ G t } Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 5 ·

Motivation TAG — More Than CFG Example (Productions) S S S T T S ⋆ c c S S a S b S S ⋆ a S ⋆ b Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 6 ·

Motivation TAG — More Than CFG Example (Productions) S S a S S T S ⋆ a S c T S S c a S b S S ⋆ a S ⋆ b Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 6 ·

Motivation TAG — More Than CFG Example (Productions) S S a S S T S ⋆ b S c S b S S a S a S b S T S ⋆ a S ⋆ b c Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 6 ·

Motivation TAG — More Than CFG Example (Productions) S S a S S T S ⋆ b S c S b S S a S a S b S T S ⋆ a S ⋆ b c String language { wcw | w ∈ Σ ∗ } Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 6 ·

Motivation TAG — Lexicalization Definition A TAG is lexicalized if each production contains a lexical item Theorem (S CHABES 1990) TAG can stronly lexicalize CFG and themselves Widespread myth J OSHI , S CHABES : Tree-adjoining grammars and lexicalized grammars. Tree Automata and Languages. North-Holland 1992 J OSHI , S CHABES : Tree-adjoining grammars. Handbook of Formal Languages. vol. 3, Springer 1997 Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 7 ·

Motivation TAG — Lexicalization Definition A TAG is lexicalized if each production contains a lexical item Theorem (S CHABES 1990) TAG can stronly lexicalize CFG and themselves Widespread myth J OSHI , S CHABES : Tree-adjoining grammars and lexicalized grammars. Tree Automata and Languages. North-Holland 1992 J OSHI , S CHABES : Tree-adjoining grammars. Handbook of Formal Languages. vol. 3, Springer 1997 Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 7 ·

Motivation TAG — Lexicalization Definition A TAG is lexicalized if each production contains a lexical item Theorem (S CHABES 1990 and K UHLMANN , S ATTA 2012) TAG can stronly lexicalize CFG and themselves but not themselves Widespread myth J OSHI , S CHABES : Tree-adjoining grammars and lexicalized grammars. Tree Automata and Languages. North-Holland 1992 J OSHI , S CHABES : Tree-adjoining grammars. Handbook of Formal Languages. vol. 3, Springer 1997 Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 7 ·

Motivation TAG — Lexicalization Definition A TAG is lexicalized if each production contains a lexical item Theorem (S CHABES 1990 and K UHLMANN , S ATTA 2012) TAG can stronly lexicalize CFG and themselves but not themselves Widespread myth J OSHI , S CHABES : Tree-adjoining grammars and lexicalized grammars. Tree Automata and Languages. North-Holland 1992 J OSHI , S CHABES : Tree-adjoining grammars. Handbook of Formal Languages. vol. 3, Springer 1997 Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 7 ·

Context-free tree grammar Overview Motivation 1 Context-free tree grammar 2 Normal forms 3 Lexicalization 4 Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 8 ·

Context-free tree grammar Context-free Tree Grammar Definition (R OUNDS 1969) ( N , Σ , S , P ) context-free tree grammar (CFTG) ranked alphabet N nonterminals ranked alphabet Σ terminals S ∈ N 0 start nonterminal P is a finite set of A ( x 1 , . . . , x k ) → r productions A ∈ N k r ∈ C N ∪ Σ ( { x 1 , . . . , x k } ) Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 9 ·

Context-free tree grammar CFTG — Example Example Productions CFTG ( N , Σ , S , P ) S → A ( α, α ) | A ( β, β ) | σ ( α, β ) N = { S ( 0 ) , A ( 2 ) } A ( x 1 , x 2 ) → A ( σ ( x 1 , S ) , σ ( x 2 , S )) Σ = { α ( 0 ) , β ( 0 ) , σ ( 2 ) } A ( x 1 , x 2 ) → σ ( x 1 , x 2 ) Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 10 ·

Context-free tree grammar CFTG — Example Example Productions CFTG ( N , Σ , S , P ) S → A ( α, α ) | A ( β, β ) | σ ( α, β ) N = { S ( 0 ) , A ( 2 ) } A ( x 1 , x 2 ) → A ( σ ( x 1 , S ) , σ ( x 2 , S )) Σ = { α ( 0 ) , β ( 0 ) , σ ( 2 ) } A ( x 1 , x 2 ) → σ ( x 1 , x 2 ) A σ � A � � σ A A � � � → σ σ S → � � � � � � x 1 x 2 α β α α x 1 x 2 β β � � � x 1 x 2 S S Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 10 ·

Context-free tree grammar CFTG — Example Example Productions CFTG ( N , Σ , S , P ) S → A ( α, α ) | A ( β, β ) | σ ( α, β ) N = { S ( 0 ) , A ( 2 ) } A ( x 1 , x 2 ) → A ( σ ( x 1 , S ) , σ ( x 2 , S )) Σ = { α ( 0 ) , β ( 0 ) , σ ( 2 ) } A ( x 1 , x 2 ) → σ ( x 1 , x 2 ) A σ � A � � σ A A � � � → σ σ S → � � � � � � x 1 x 2 α β α α x 1 x 2 β β � � � x 1 x 2 S S Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 10 ·

Context-free tree grammar CFTG — Derivation Example Example A σ � � � σ A A A � � � → σ σ S → � � � � � α β � x 1 x 2 x 1 x 2 α α β β � � � x 1 x 2 S S A A σ A σ σ σ σ σ σ A σ σ ⇒ G ⇒ G ⇒ G ⇒ G ⇒ ∗ S G α σ α σ α α A S α α σ α α A α α S S β β α β β β β β α β Strong Lexicalization of Tree-Adjoining Grammars A. Maletti and J. Engelfriet 11 ·