Extensions

1. Extensions ESSLLI02

2. Other extensions • Influenced by Merge and Move analysis

3. Minimalism and Formal Grammars Several attempts to formalise « minimalist principles »: • Stabler, 1997, 1999, 2000, 2001: - « minimalist grammars » (MG) • Weak equivalence with: - Multiple Context-Free Grammars (Seki et al. Harkema) - Linear Context-Free Rewriting Systems (Michaelis)

4. Results from formal grammars • Mildly context-sensitivity • Equivalence with multi-component TAGs (Weir, Rambow, Vijay-Shankar) • Polynomiality of recognition

5. minimalist grammars • Lexical items are considered lists of features • select* licensors* base licensees* P*I* • select: =n, =d, =v, =t, … • base: n, d, v, t, … • licensors: +k, +wh, … • licensees: -k, -wh, …

6. Example (Stabler 97) Lexicon: d –k maria d –k quechua =n d –k some =n d –k every n student n language =d +k =d v speaks =c +k =d v believes =v +K t =t c =t c -k

7. Merge =n d –k every n language

8. < d –k every language

9. < =d +k =d v speaks d –k every language

10. < < +k =d v speaks –k every language

11. < –k every language Move < +k =d v speaks

12. < –k every language Move < < +k =d v speaks –k every language

13. > < every language Move < l =d v speaks

14. > < (every) (language) < =d v speaks /every//language/ LF : (some linguist)(every language)(speaks) PF: /some linguist speaks every language/

15. A logical reformulation 1- MERGE Let us assume: |- every : d/n every : language: |- language : n speaks: |- speaks : (d\v)/d where / and \ are « logically » the same, they only differ by labelling conventions

16. cf. (natural deduction style)

17. commutative product : the order of formulae in the antecedent is not relevant • word order supposed to be induced from the dominance relations in the proof-tree (the highest, the leftest) • words = extra-logical axioms • sequents combined by [/E], [\E] and …

18. speaks every language: d\v every language:d speaks: (d\v)/d every:d/n language:n

19. 2 - MOVE Move may be decomposed into two phases: 1) to assume hypotheses 2) to discharge them by means of a product

20. Ä k d (k \ (d \ v))/d Let us assume: |- every language : (= every DP needs a case feature) |- speaks : ( a V is a case-assigner)

21. speaks : (k \ (d \ v))/d x : d x : d a a y : k y : k x : d speaks _ x : k \ (d \ v) a a y_speaks_x y : k ; x : d : d \ v a Ä every language : k d y : k ; x : d y _ speaks _ x : d \ v a a < > < > every language _ speaks _ every language : d \ v a 1 2 1) Assuming hypotheses (x, y): 2) Discharging hypotheses:

22. y_speaks_x d\v k\(d\v) k y (k\(d\v))/d d speaks x 1) Assuming hypotheses speaks_x

23. y_speaks_x d\v d\v <ev lang>_speaks_<ev lang> k\(d\v) k Ä k d y (k\(d\v))/d d speaks x 2) Discharging hypotheses every_language speaks_x

24. <ev_lang>_speaks_<ev_lang> d\v k\(d\v) k Ä k d y (k\(d\v))/d d speaks x Or (proof-net): speaks_x every_language

25. y_speaks_x d\v k\(d\v) k y (k\(d\v))/d d speaks x this translates movement: speaks_x

26. Tensor elimination

27. speaks_ev_lang d\v k\(d\v) k Ä k d y (k\(d\v))/d d speaks x SVO : speaks_x every_language

28. <ev_lang>_speaks d\v k\(d\v) k Ä k d y (k\(d\v))/d d speaks x SOV speaks_x every_language

29. Tensor elimination

30. )/n whkd which: which : ( a a book: book: n do : (wh\cp)/t ((k\t)/vp) a do:  you: kd a you: think: think : (d\vp)/t a a Mary: Mary :kd reads: reads : (k\t)/vp) ((k\(d\vp))/d) a 

31. x’’think Mary reads z:vp think Mary reads z:d\vp Mary reads z:t reads x’z:k\t x’z<reads>:vp z<reads>:d\vp y<reads>x:d\vp <reads>x:k\(d\vp) reads:(k\t)/vp k\(d\vp)/d  x’’:d think:(d\vp)/t y’:k <reads>2:(k\t)/vp x’:d z:kd y:k x:d <reads>: k\(d\vp)/d

32. Which book do you think Mary reads:cp do you think Mary reads z:wh\cp think Mary reads z:d\vp x’’:d you<do>think Mary reads z:t Mary reads z:t think:(d\vp)/t <do>x’’think Mary reads z:k\t reads x’z:k\t y’:k x’z<reads>:vp <reads>2:(k\t)/vp x’:d z<reads>:d\vp z:kd u:wh <do>2:(wh\cp)/t y’’:k <do>:(k\t)/vp x’’think Mary reads z:vp

33. Conditions on proofs • To be synchronized with semantic proofs

34. k mary k\ip (k\ip)/vp seems vp vp vp/vp (k\ip)/vpvp/vp np np\vp to work knp

35. k1 mary k\ip (k\ip)/vp2 seems vp vp vp/vp2 np1 np\vp to work

36. vp vp/vp2 np1 np\vp to work k1 mary k\ip (k\ip)/vp2 seems vp

37. t (et)t u.u(mary) et t (((tt)t)t) Q.Q(u.PRES(seem(u))) (tt)t P(work(x)) t t work(x) tt P e  t y.work(y) e x Homomorphism of types

38. t PRES(seem(work(mary))) (et)t u.u(mary) et x.PRES(seem(work(x))) t PRES(seem(work(x))) (((tt)t)t) Q.Q(u.PRES(seem(u))) (tt)t P.P(work(x)) P(work(x)) t t work(x) tt P e  t y.work(y) e x Semantical deduction in MILL

39. parameters… • English: • I did prepare a (one) meal • Tibetan: • nga neka ci sö payin • (litt. I meal one prepare did)

40. ip k I k\ip (k\ip)/vp did vp k k\vp np np\(k\vp) np (np\(k\vp))/np prepare knp (knp)/n a n meal

41. knp (knp)/n a n meal

42. knp n neka n\(knp) ci

43. knp n neka n\(knp) ci vp k k\vp np np\(k\vp) np (np\(k\vp))/np prepare

44. knp n neka n\(knp) ci vp k k\vp np np\(k\vp) np (np\(k\vp))/np sö

45. knp n neka n\(knp) ci vp k k\vp np np\(k\vp) np  (np\(k\vp))/np sö

46. knp n neka n\(knp) ci ip k I k\ip (k\ip)/vp did vp k k\vp np np\(k\vp) np  (np\(k\vp))/np sö

47. ip k\ip k nga knp n neka n\(knp) ci vp\(k\ip) payin vp k k\vp np np\(k\vp) np  (np\(k\vp))/np sö

48. ip k I k\ip (k\ip)/vp did vp k k\vp np np\(k\vp) np (np\(k\vp))/np prepare knp (knp)/n a n meal

49. ip k\ip k nga knp n neka n\(knp) ci vp\(k\ip) payin vp k k\vp np np\(k\vp) np  (np\(k\vp))/np sö

50. Proof-Net techniques np\vp + meet mary (np\(k\vp))/np – meet knp – Mary