Notes on TAG (LTAG) and Feature Structures Aravind K. Joshi April

S NP  V likes NP  e S VP S NP  V S*  think VP  V S does S* NP  who Harry Bill     substitution adjoining who does Bill think Harry likes LTAG: A Derivation

Constraints on Substitution and Adjoining S NP  V likes VP NP  Harry    requires a singular NP tree to be substituted at the NP node in 

S NP  V likes NP  e S VP S NP  V S*  think VP  V S does S* NP  who Harry Bill     Constraints on Substitution and Adjoining  can be adjoined to  at the root node of  because  is anchored on an untensed verb think

S NP  V likes NP  e S VP S NP  V S*  think VP  V S does S* NP  who Harry Bill     The tense associated with the root node of  comes from the tense associated with  and not from likes Constraints on Substitution and Adjoining: Feature Passing

Feature Structures Feature Structures: Attribute-Value Structures X1 f: a g: b h: c X2 f: a g: b X1 has more information than X2 X1 is more specific than X2

Feature Structures Values can be atomic or complex cat: NP agreement: number: sing gender: masc person: third Recursion in Feature Structures There is no recursion in the feature structures in LTAG Thus, in principle, FS can eliminated at the expense of multiplying non-terminals

Feature Structures Feature Structures: Attribute-Value Structures X1 f: a g: a X2 f: a g: X2 has more information than X1 X2 is more specific than X1 X2 subsumes X1 Co-indexing can be across feature structures also

Unification of feature structures Given two FS, X1 and X2 X3 = X1 U X2 where X3 is the least FG which subsumes both X1 and X2 X3 is obtained by unifying X1 and X2

Constraints on Substitution Feature Passing S NP  V likes VP NP  Harry    requires a singular NP tree to be substituted in  [num: sing] [num: ] [num: sing] [num: ]

S NP  V likes NP  e S VP S NP  V S*  think VP  V S does S* NP  who Harry Bill     The tense associated with the root node of  comes from the tense associated with  and not from likes Constraints on Adjoining: Feature Passing [t: ut] [t: ] [t: ut] [t: ] [t: pres] [t: ]

Top and Bottom Feature Structures We need top (t) and bottom (b) feature structures for each node, especially the internal nodes of a tree. Why? For each node we have a top and bottom view from that node– adjoining can pull apart these two views. After the derivation stops we unify the top and bottom FS at each node. If one of these unifications fails then the derivation crashes.

Feature Structures and Unification Adjoining as unification  X  X* X  X X tbtb trbrtrbr tfbftfbf t  t r brbr b  b f tftf 

Feature Structures and Unification Adjoining as unification  X  X* X  X X tbtb trbrtrbr tfbftfbf t  t r brbr b  b f tftf 

Feature Structures and Unification Adjoining as unification (Adjoining at the root node)  X  X* X  X tbtb trbrtrbr tfbftfbf t  t r brbr b  b f tftf  X 

Feature Structures and Unification :: X  X  X t trbrtrbr t  t r brbr  Substitution as unification

Obligatory (adjoining) constraints John tried to swim S NP  V S* tried VP [ t: -] [ t: ] S PRO TO V to VP swim [t: ] [ t: - ] [ t: +] [t: ] [ t: +] [t: ]  If nothing is adjoined to  then  will crash because the top and bottom features at the root node of  will not unify

Obligatory (adjoining) constraints John tried to swim S NP  V S* tried VP [ t: -] [ t: ] S PRO TO V to VP swim [t: ] [ t: - ] [ t: +] [t: ] [ t: +] [t: ] 

Adjoining  to the root of  John tried to swim S NP  V S* tried VP [ t: -] [ t: ] S PRO TO V to VP swim [t: ] [ t: - ] [ t: +] [t: ] [ t: +] [t: ]   Note that the conflicting features at the root node of  are now separated