Approches%20formelles%20en%20syntaxe%20et%20s

1
Approches formelles en syntaxe et sémantique

• Alain Lecomte
• UMR 7023
• Structures Formelles de la Langue

2
programme minimaliste

• Deux opérations générales
• merge
• move

3
definition

• A minimalist grammar is a 4-tuple (V, Cat, Lex,
  F) where
• V P ? I
• Cat (base ? select ? licensee ? licensor),
• Lex cf. above
• F merge, move
• ex P /marie/, /pierre/, /le/,/quechua/,
• I (marie), (pierre), (quechua), (le),
• base c, t, v, d, n,
• select x x?base
• licensee -k, -wh,
• licensor k, K, wh, WH,

4
merge

• A pair of trees ?, ? belongs to the domain of
  merge iff ? has the feature x and ? has the
  feature x for some x?base.
• merge(?, ?) lt ?, ? if ? has only one node
• merge(?, ?) gt ?, ? if ? has more than one
  node
• ? ? - x and ? ? - x
• ?  has the feature f  the first element of
  the sequence which labels ? s head is f

5
projections, heads

• When two constituants are merged, one of them
   projects over  the other, we write x lt y for
   x projects over y 
• x is head of y if
• y leaf and x y
• or x is head of some z which projects over all
  its sisters

6
move

• ? belongs to the domain of move iff ? has the
  feature y and ? has exactly one maximal subtree
  ?0 which has the feature y
• move(?) gt ?0 , ?
• where ?0 is ?0 -y and ? is ? - y and ?0
  is replaced by a featureless node if y is strong
  and with only the phonetic features if it is
  weak.
• maximal his root is the maximal projection of
  some head

7
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
8
Merge
n d k every
n language
9
(No Transcript)
10
lt
d k d v speaks
d k every
language
11
lt
lt
k d v speaks
k every
language
12
Move
lt
k d v speaks
13
Move
lt
lt
k d v speaks
k every
language
14
Move
lt
l
d v speaks
15
lt
d v speaks
/every//language/
LF (some linguist)(every language)(speaks)
PF /some linguist speaks every language/
16
merge

• Peter smoke (sans tenir compte du temps)

n /peter/
n v /smoke/
17
merge

• Peter smoke

/peter/
v /smoke/
18
merge

• Peter smoke
• Type driven interpretation

t
/peter/ e
v /smoke/ e ? t
19
merge

• Peter smoke (without tense)
• Type driven interpretation

t smoke(p)
/peter/ e
v /smoke/ e ? t ?x. smoke(x)
p
20
Merge principle

• Two expressions can merge only if their
  semantical types allow it
• If ? and ? are expressions, if ? has the type of
  a function the domain of which contains ?, then
  they can merge and the resulting expression ? is
  such that
• ? ?(?)
• (with the resulting type)

21
move

• personne que Pierre admire

N
N
CP
personne
que
C
IP
C
Pierre admire t
22
move

• personne que Pierre admire
• ?x. personne(x)?admire(pierre, x)
• Hypothesis (Heim Kratzer)
• every trace translates into an e-type variable
  (if an NP is moved)
• Pierre admire t
• admire(pierre, xn)

23
move

• personne que Pierre admire

N
N
CP ?P.?x. P(x)?admire(pierre, x)
personne
que
C
IP
C
admire(pierre, x)
Pierre admire t
24
move

• personne que Pierre admire

N
N
CP ?P.?x. P(x)?admire(pierre, x)
personne
que
C
?U. ?P.?x. P(x)?U(x)
IP
C
admire(pierre, x)
Pierre admire t
25
move

• personne que Pierre admire

N
N
CP ?P.?x. P(x)?admire(pierre, x)
personne
?
que
C
?U. ?P.?x. P(x)?U(x)
IP
C
admire(pierre, x)
Pierre admire t
26
types

N
lte, tgt
N
CP ?P.?x. P(x)?admire(pierre, x)
personne
t
que
C
?U. ?P.?x. P(x)?U(x)
ltlte, tgt, ltlte, tgt, lte, tgtgtgt
IP
C
admire(pierre, x)
Pierre admire t
27
types

N
lte, tgt
N
CP ?P.?x. P(x)?admire(pierre, x)
personne
mismatch
t
que
C
?U. ?P.?x. P(x)?U(x)
ltlte, tgt, ltlte, tgt, lte, tgtgtgt
IP
C
admire(pierre, x)
Pierre admire t
28
types

lte, tgt
Abstraction step
t
C
IP
C
admire(pierre, x)
Pierre admire t
29
types

lte, tgt
?x. admire(pierre, x)
t
C
IP
C
admire(pierre, x)
Pierre admire t
30
Move principle

• Let ?f a tree which has the feature f, and
  which contains only one maximal subtree ?-f,
  therefore of semantics ?(x?), where x? is a
  variable representing ?.
• Let ? the tree obtained by moving ? out of ?,
  then
• ? ?(?x. ?(x?)x?/x), if there is
  no further expected move of ?.
• If there are expected moves of ? (other licensees
  f in it),
• ? (?x. ?(x?)x?/x)(y) where y is a
  fresh variable

31
example

• Quel bus tu prends?
• Lexicon
• bus n /bus/ ?x.bus(x)
• quel n d wh /quel/ ?P.?Q.quel x P(x)?Q(x)
• tu d /tu/ tu
• prends d d v /prends/ ?x.?y.monte-dans(y, x)
• v t
• t WH c

32
n /bus/ ?x.bus(x)
n d wh /quel/ ?P.?Q.quel x P(x)?Q(x)
33
lt
/bus/ ?x.bus(x)
d wh /quel/ ?P.?Q.quel x P(x)?Q(x)
merge
34
?Q.quel x bus(x)?Q(x)
lt
/bus/
d wh /quel/
merge
35
d -wh /quel//bus/ xbus,
d d v /prends/ ?x.?y.monte-dans(y, x)
merge
36
?y.monte-dans(y, xbus )
lt
-wh /quel//bus/
d v /prends/
merge
37
gt
?y.monte-dans(y, xbus )
lt
d /tu/ tu
-wh /quel//bus/
d v /prends/
merge
38
monte-dans(tu, xbus )
gt
lt
/tu/
-wh /quel//bus/
v /prends/
merge
39
monte-dans(tu, xbus )
lt
gt
v t
lt
/tu/
-wh /quel//bus/
v /prends/
merge
40
monte-dans(tu, xbus )
lt
gt
t
lt
/tu/
-wh /quel//bus/
/prends/
merge
41
monte-dans(tu, xbus )
lt
lt
t WH c
gt
t
lt
/tu/
-wh /quel//bus/
/prends/
merge
42
monte-dans(tu, xbus )
lt
lt
WH c
gt

lt
/tu/
-wh /quel//bus/
/prends/
merge
43
gt
monte-dans(tu, xbus )
lt
-wh /quel//bus/
lt
WH c
gt

lt
/tu/
/prends/
?
move
44
gt
monte-dans(tu, xbus )
lt
/quel//bus/
lt
c
gt

lt
/tu/
/prends/
?
move
45
?u. monte-dans(tu, u )
?Q.quel x bus(x)?Q(x)
lt
lt
c
gt

lt
/tu/
/prends/
?
move
46
quel x bus(x)? monte-dans(tu, x )
lt
lt
c
gt

lt
/tu/
/prends/
?
move
47
conclusion

• Syntax and semantic cooperate
• merge and move drive semantical operations
  (application and abstraction)
• semantical typing selects the correct derivations
  ( objects  go to accusatives,  subjects  to
  nominatives)
• Similarities with type-logical grammars
• resource consumption logic
• Curry-Howard homomorphism

48
Passive voice

• seen d v lte, tgt
• ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? e)
• Mary d -k
• by d obl V v lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

49

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? e)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

d v lte, tgt
d k e
/seen/
50

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

51

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

seen(x)
v NOM infl
/was/
v lte, tgt
k e
/seen/
52

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

seen(x)
seen(x)
NOM infl
/was/
lte, tgt
k e
/seen/
53

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

-k
seen(x)
/Paul/
seen(x)
NOM infl
/was/
lte, tgt
/seen/
54

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

seen(x)
/Paul/
seen(x)
infl
/was/
lte, tgt
/seen/
55

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

?x.seen(x)
/Paul/
?P. P(paul)
seen(x)
seen(x)
infl
/was/
lte, tgt
e
/seen/
56

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

seen(Paul)
?x.seen(x)
/Paul/
?P. P(paul)
seen(x)
seen(x)
infl
/was/
lte, tgt
e
/seen/
57

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

d k
d obl V v
/Mary/
/by/
58

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

k
obl V v
/Mary/
/by/
59

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

-k
(Mary)
obl V v
/Mary/
/by/
60

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

(Mary)
V v
/Mary/
/by/
61

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

k e
v lte, tgt
(Mary)
/seen/
V v
/Mary/
/by/
62

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

k e
lte, tgt
(Mary)
/seen/
v
/Mary/
/by/
63

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

k e
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
v
/Mary/
/by/
64

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

agent(seen(x), mary)
?y.agent(seen(y), mary)
k x e
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
v
/Mary/
/by/
65

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

v NOM infl /was/
agent(seen(x), mary)
?y.agent(seen(y), mary)
k x e
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
v
/Mary/
/by/
66

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

NOM infl /was/
agent(seen(x), mary)
?y.agent(seen(y), mary)
k x e
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
/Mary/
/by/
67

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

-k /Paul/
NOM infl /was/
agent(seen(x), mary)
?y.agent(seen(y), mary)
x
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
/Mary/
/by/
68

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

/Paul/
?x. agent(seen(x), mary)
infl /was/
agent(seen(x), mary)
?y.agent(seen(y), mary)
x
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
/Mary/
/by/
69

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

/Paul/
?P. P(paul)
?x. agent(seen(x), mary)
infl /was/
agent(seen(x), mary)
?y.agent(seen(y), mary)
x
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
/Mary/
/by/
70

• seen d v lte, tgt ?x. seen(x)
• was v NOM infl ltt, tgt
• Paul d k (ltlte, tgt, tgt ? t)
• Mary d -k
• by d obl V V lte, ltlte, tgt, lte, tgtgtgt
• ?z.?u.?y.agent(u(y), z)

agent(seen(paul), mary)
/Paul/
?P. P(paul)
?x. agent(seen(x), mary)
infl /was/
agent(seen(x), mary)
?y.agent(seen(y), mary)
x
?u.?y.agent(u(y), mary)
?x. seen(x)
lte, tgt
(Mary)
/seen/
/Mary/
/by/