1. MC-TAG, flexible composition, etc. ARAVIND K. JOSHI March 15 2006

2. 2 Feature Structures and Unification Adjoining as unification  X  X* X  X X tbtb trbrtrbr tfbftfbf t  t r brbr b  b f tftf  No directionality involved in the composition

3. 3 Feature Structures and Unification :: X  X  X t trbrtrbr t  t r brbr  Substitution as unification No directionality involved in the composition

4. 4 Flexible Composition (FC) All formal grammars (FG) have some notion of FC However, it is not the case that for all FG, FC is productive, in the sense that -- FC gives to new and useful derivations and/or -- new word order variations, scope ambiguities, for example In a CFG, a rule such as A B C either B is a function taking C as the argument or vice versa, i.e., A (A/C) C or A B (B\A) -- same derived tree, different derivations, but not useful -- same word order

5. 5 Flexible Composition (FC) CFG rules as one level trees a1: S NP3 VP3 a2: S NP2 S VP2 a3: S NP1 S VP1 a1: S NP3 VP3 a2: S NP2 S VP2 a3: S NP1 S VP1 Same derived tree, two different derivations Same word order NP1 NP2 NP3 VP3 VP2 VP1 Structure adjacency (for one level tree structures) does not buy anything more

6. 6 Standard TAG Derived Tree Derivation tree -- different ways of walking over the derivation tree -- top-down -- bottom-up -- inside-out -- It does not make any difference in terms of the the set of strings that can be derived

7. 7 Multi-Component TAG (MC-TAG) Different motivations Tree-local -- Tree-local MC-TAG weakly equivalent to Standard TAG Set-local

8. 8 Flexible Composition  X Split  at x X X  supertree of  at X  subtree of  at X Adjoining as Wrapping

9. 9  X  X X  X X   wrapped around  i.e., the two components  and  are wrapped around   supertree of  at X  subtree of  at X Flexible Composition Adjoining as Wrapping

10. 10 S V NP  likes NP(wh)  e S VP S NP  V S*S*  think VP  substitution adjoining Flexible Composition Wrapping as substitutions and adjunctions NP  - We can also view this composition as  wrapped around  - Flexible composition

11. 11 S* V NP  likes NP(wh)  e S VP S NP  V S*S*  think VP  substitution adjoining Flexible Composition Wrapping as substitutions and adjunctions NP    S   and  are the two components of   attached (adjoined) to the root node S of   attached (substituted) at the foot node S of  Leads to multi-component TAG (MC-TAG)

12. 12  Multi-component LTAG (MC-LTAG)     The two components are used together in one composition step. Both components attach to nodes in  an elementary tree. This preserves locality.

13. 13 Tree-Local Multi-component LTAG (MC-LTAG) - How can the components of MC-LTAG compose preserving locality of LTAG - Tree-Local MC-LTAG -- Components of a set compose only with an elementary tree or an elementary component - Flexible composition -- The notion of the derivation tree still holds for the Tree-Local MC-TAG -- Different ways of walking over the derivation tree -- It can make a difference in terms of the structures that can be derived!

14. 14 Tree-Local MC-LTAG and flexible semantics Three clauses, C1, C2, and C3, each clause can be either a single elementary tree or a multi- component tree set with two components The verb in C1 takes the verb in C2 as the argument and the verb in C2 takes the verb in C3 as the argument Flexible composition allows us to compose the three clauses in three ways

15. 15 Tree-Local MC-LTAG and flexible semantics Three ways of composing C1, C2, and C3 C1 C2 C3 C1 C2 C3 C1 C2 C3 (1) (2) (3) The third mode of composition can give rise to new strings, which are not obtainable from the first two ways only

16. 16 Scrambling: N3 N2 N1 V3 V2 V1 VP N3 VP VP N3 e V3 VP N2 VP VP N2 V2 e VP N1 VP VP N1 V1 e VP

17. 17 Scrambling: N3 N2 N1 V3 V2 V1 VP N3 VP VP N3 e V3 VP N2 VP VP N2 V2 e VP N1 VP VP N1 V1 e VP (flexible composition)

18. 18 Tree-local MC-TAG Usually two components only One component can be lexically empty (null) Components are not independent -- immediate domination -- domination -- co-indexing Flexible composition has to respect these constraints -- some examples -- Scrambled NP’s -- Extraposition from NP

19. 19 (1) The gardener who the woman kept calling all day finally came. (1’) The gardener finally came who the woman kept calling all day. (2) The gardener who the woman who had lost her keys kept calling all day finally came. *(2’) The gardener who the woman kept calling all day finally came who had lost her keys. Extraposition from NP: An example

20. 20 NP VP The gardener finally came S NP VP The gardener finally came S S S who the woman kept calling all day

21. 21 NP VP The gardener finally came S NP VP The gardener finally came S S S who the woman kept calling all day b1: { b11 b12} NP S NP* S(i) S* S(i) e who the woman kept calling all day

22. 22 NP VP The gardener finally came S NP VP The gardener finally came S S S who the woman kept calling all day b1: { b11 b12} NP S NP* S(i) S* S(i) e who the woman kept calling all day Tree local MC-LTAG for NP Extraposition

23. 23 NP VP S S S (i) who had lost her keys NP S The gardener who the woman (i) kept calling all day finally came * (2) The gardener who the woman who had lost her keys kept calling all day finally came. *(2’) The gardener who the woman kept calling all day finally came who had lost her keys. Not possible even with flexible composition if the constraints between the two components are to be respected