1. A Computational Approach to Minimalism Alain LECOMTE INRIA-FUTURS (team SIGNES) & CLIPS-IMAG (Grenoble)

2. 22/12/2003ICON 2003 - Alain Lecomte2 minimalism the current trend in Generative Syntax (Chomsky, 1995, 1998, 2001) Minimalist grammars : Stabler, 1997, 1999, 2001 etc. Categorial grammars : Morrill, 1995, Moortgat, 1997, Lambek, 1958, 1988 etc. CG and MG : Lecomte and Retoré, 1999, 2001, 2002 etc.

3. 22/12/2003ICON 2003 - Alain Lecomte3 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. 22/12/2003ICON 2003 - Alain Lecomte4 Results from formal grammars Weak equivalence with: - Multiple Context-Free Grammars (Seki et al. Harkema) - Linear Context-Free Rewriting Systems (Michaelis) Mildly context-sensitivity Equivalence with multi-component TAGs (Weir, Rambow, Vijay-Shankar) Polynomiality of recognition

5. 22/12/2003ICON 2003 - Alain Lecomte5 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. 22/12/2003ICON 2003 - Alain Lecomte6 Example (Stabler 97) Lexicon: d –k maria =n d –k some n student =d +k =d v speaks =v +K t =t c d –k quechua =n d –k every n language =c +k =d v believes =t c -k

7. 22/12/2003ICON 2003 - Alain Lecomte7 Merge merge(t1[=c], t2[c]) = [< t1, t2 ] if t1  Lex merge(t1[=c], t2[c]) = [> t2, t1 ] if not. merge(t1[=C], t2[c]) = [< t1(phon(t1)^phon(t2)), t2(phon(e)) ] if t1  Lex merge(t1[C=], t2[c]) = [< t1(phon(t2)^phon(t1)), t2(phon(e)) ] if t1  Lex

8. 22/12/2003ICON 2003 - Alain Lecomte8 Move Let t* the maximal projection of a head t. Let, for each t1, t2, such that t strictly contains t1 but does not contain t2: t{t1/t2} the result of replacing t1 by t2 inside t, then : for all expression t1[+f] which contains only one maximal subtree t2[-f]* : move(t1[+f]) = [> t2*, t1{ t2[-f]* / }] where is the tree with only an empty node.

9. 22/12/2003ICON 2003 - Alain Lecomte9 with weak and strong features move(t1[+F]) = [> t2*, t1{ t2[-f]* / }] move(t1[+f]) = [> t2(phon(e))*, t1{ t2[-f]* / t2’* }] where t2’ is t2* from which all the non phonetic features have been suppressed.

10. 22/12/2003ICON 2003 - Alain Lecomte10 example see : =d +acc =d v /see/ a : =n d –case /a/ movie : n /movie/

11. 22/12/2003ICON 2003 - Alain Lecomte11 =n d –k every n language Merge

12. 22/12/2003ICON 2003 - Alain Lecomte12 d –k every language <

13. 22/12/2003ICON 2003 - Alain Lecomte13 d –k every language < =d +k =d v speaks

14. 22/12/2003ICON 2003 - Alain Lecomte14 –k every language < +k =d v speaks <

15. 22/12/2003ICON 2003 - Alain Lecomte15 –k every language < +k =d v speaks < Move

16. 22/12/2003ICON 2003 - Alain Lecomte16 –k every language < +k =d v speaks < Move –k every language <

17. 22/12/2003ICON 2003 - Alain Lecomte17 every language < =d v speaks < Move >

18. 22/12/2003ICON 2003 - Alain Lecomte18 [e /] :  x :A/B   y : B ,  xy : A [e \] :   y : B  x :B\A ,  yx : A [i  ] :  x : A   y : B ,  (x, y) : A  B [e  ] :  w : A  B , x : A, y : B,  ’  z : C , ,  ’  let(x, y) = (  1(w),  2(w)) in z : C

19. 22/12/2003ICON 2003 - Alain Lecomte19 condition on proofs Selected proofs are such that: hypotheses are discharged in the order they are introduced (first in, first out) This translates the short movement constraint (and improves parsing)

20. 22/12/2003ICON 2003 - Alain Lecomte20 Categorial version see :  /see/ : (acc\v) /d a :  /a/ : (case  d)/n movie :  /movie/ : n

21. 22/12/2003ICON 2003 - Alain Lecomte21 proof  /see/ : (acc\v)/d x :d  x :d  /a/ : (cas  d)/n  /movie/ : n y : acc  y : acc x : d  /see/ x : acc \ v  /a movie/ : (cas  d)y : acc, x : d  y /see/ x : v   1(/a movie/) /see/  2(/a movie/) : v

22. 22/12/2003ICON 2003 - Alain Lecomte22 Definition : merge = [e \] or [e /] and move = [e  ], where / and \ are the residuates of the commutative product , simply labelled differently from each other with regards to the phonetic features that they combine.

23. 22/12/2003ICON 2003 - Alain Lecomte23 lexicon what :  /what/ : (wh   (cas  d))/n book :  /book/ : n  : (  wh\cp)/ip  you :  /you/ : nom  d read :  /read/ :  (  nom\ip)/vp  (d\(acc\vp))/  d (abbreviated in  I  VP)

24. 22/12/2003ICON 2003 - Alain Lecomte24 deduction U : (d\(acc\vp))/  d x : d(1) y : dU  x : d\(acc\vp)(2) z :cas yU  x : acc\vp(3) u : cas  dz yU  x : vp(4) V :(  nom\ip)/vpyU  u : vp(5) /read/ :  I  VPVyU  u : :  nom\ip(6) /read/y  u :  nom\ip(7) and then : z’ :cas/read/ y  u :  nom\ip(8) /you/ : nom  d  z’/lis/ y  u : ip(9)  : (  wh\cp)/ip/you read/  u : ip(10) u’ :wh /you read/  u :  wh\cp(11) /what book/ : wh   (cas  d)  u’/you read/  u : cp (12) /what book you read/ : cp

25. 22/12/2003ICON 2003 - Alain Lecomte25 parameters khyerang :  /khyerang/ : nom  d khapar :  /khapar/ : wh  cas  d thrung :  /thrung/ : (d\(  obl\vp))/d pare:  /pare/ :  (ip\(cp/wh))  vp\(  nom\ip) compared with: you:  /you/ : nom  d where:  /where/ : wh   (cas  d) born:  /born/ : (d\(obl\vp))/  d were:  /were/ : (  wh\cp)/ip   (  nom\ip)/vp

26. 22/12/2003ICON 2003 - Alain Lecomte26 deduction /thrung/ : (d\(  obl\vp))/d x : d y: d /thrung/x : d\(  obl\vp) z : casey/thrung/x :  obl\vp u : case  d  zy/thrung/x : vp  uy/thrung/ : vp U : vp\(  nom\ip) z’: case  uy/thrung/U:  nom\ip /khyerang/ : nom  d  z’  uy/thrung/U: ip /khyerang/  u/throng/U: ipV:  (ip\(cp/wh)) /pare/: C  I/khyerang/’  u/thrung/U  V: cp/wh /khyerang/  u/throng pare/: cp/wh v: wh /khapar/: wh  cas  d /khyerang/  u/throng pare/v: cp /khyerang khapar throng pare/: cp

27. 22/12/2003ICON 2003 - Alain Lecomte27 Conclusion A theoretical goal : in what extent the syntactic system of language is a process of resource consumption, A practical goal : in what extent such theories can be logically implementable in logical frameworks (Coq…)