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Transcript of We are taking the language L to be a way of computing expressions, a recursive definition of a set...
![Page 1: We are taking the language L to be a way of computing expressions, a recursive definition of a set EXP. (i) a set of features (ii) principles for assembling.](https://reader035.fdocuments.us/reader035/viewer/2022062511/551d9d8c497959293b8c1e41/html5/thumbnails/1.jpg)
We are taking the language L to be a way of computing expressions, a recursive definition of a set EXP.
•(i) a set of features
•(ii) principles for assembling features into lexical items
Thus, UG might postulate that FL provides:
•(iii) operations that apply successively to form syntactic objects of greater complexity; call them CHL, the computational system for human language
Sémantique et Grammaire Générative
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Which book do you think that Mary read?
Énumération: which, book, Mary, think, that, you, do
Dérivation
Forme « phonologique » Forme « logique »
/witbukdujuinkǽtmerired/ quel x, x = livre, tu penses que marie a lu x
Exemple
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Irene Heim & Angelika Kratzer, Semantics in Generative Grammar
Associer des contreparties sémantiques non plus à des « règles » mais à des principes généraux tels que:
- merge
- move
Heim & Kratzer, 1998
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exemple
Which book do you think that Mary read?
Forme « logique »
quel x, x = livre, tu penses que marie a lu x
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exemple
Forme « logique »
a_lu: z. y. a_lu(y,z)
marie:D
penser:x. y. penser(y,x)
tu:D
livre:x.livre(x)
quel:?
Which x (x = book) do you think that Mary read x
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exemple
Forme « logique »
[z. y. a_lu(y,z)](x) ->y.a_lu(y, x)
tu:D
quel:?
Which x (x = book) do you think that Mary read x
penser:x. y. penser(y,x)
livre:x.livre(x)
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exemple
Forme « logique »
tu:D
quel:?
Which x (x = book) do you think that Mary read x
livre:x.livre(x)
penser:x. y. penser(y,x)
[y.a_lu(y, x)](Marie) ->a_lu(Marie, x)
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exemple
Forme « logique »quel:?
Which x (x = book) do you think that Mary read x
a_lu(Marie, x)
penser:[x. y. penser(y,x)](a_lu(Marie, x) ->y. penser(y, a_lu(Marie, x))
livre:x.livre(x)
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exemple
Forme « logique »quel:?
Which x (x = book) do you think that Mary read x
a_lu(Marie, x)livre:x.livre(x)
penser:[y. penser(y, a_lu(Marie, x))](tu) ->penser(tu, a_lu(Marie, x))
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après?
Forme « logique »quel:?
Which x (x = book) do you think that Mary read x
livre:x.livre(x)
penser:penser(tu, a_lu(Marie, x))
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proposition
quel:?
livre:x.livre(x)
penser:penser(tu, a_lu(Marie, x))
x. penser(tu, a_lu(Marie, x))
quel(x, livre(x) penser(tu,a_lu(Marie, x))
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proposition
quel:?
livre:x.livre(x)
penser:penser(tu, a_lu(Marie, x))
x. penser(tu, a_lu(Marie, x))
quel(x, livre(x) penser(tu,a_lu(Marie, x))
Une fonction ayant pour arguments deux propriétéset qui retourne une proposition sous forme de question
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problème
• D’où vient le pas d’abstraction :
penser:penser(tu, a_lu(Marie, x))
x. penser(tu, a_lu(Marie, x))
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SNwhich book
CP
C’
Cdo
SNyou
Vthink
that
SNMary
Vread
SNt
VP
CP
V’
V’
VP
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SNwhich book
CP
C’
Cdo
SNyou
Vthink
that
SNMary
Vread
SNt
VP
CP
V’
V’
VP
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SNwhich book
CP
C’
Cdo
SNyou
Vthink
that
SNMary
Vread
SNt
VP
CP
V’
V’
VP
t<<e, t>, t>P.?(x, book(x) & P(x))
think(you, read(mary, x))
TYPE MISMATCH
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SNwhich book1
CP
C’
Cdo
SNyou
Vthink
that
SNMary
Vread
SNt1
VP
CP
V’
V’
VP
t<<e, t>, t>P.?(x, book(x) & P(x))
think(you, read(mary, x))1
x. think(you, read(mary, x))
BINDER
<e, t>
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SNwhich book1
CP
C’
Cdo
SNyou
Vthink
that
SNMary
Vread
SNt1
VP
CP
V’
V’
VP
t<<e, t>, t>P.?(x, book(x) & P(x))
think(you, read(mary, x))
x. think(you, read(mary, x))
OU BIEN…
<e, t>
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SNwhich book1
CP
Cdo
SNyou
Vthink
that
SNMary
Vread
VP
CP
V’
V’
VP
tROTATE !!!!
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SNwhich book1
CP
Cdo
SNyou
Vthink
that
SNMary
Vread
VP
CP
V’
V’
VP
xceci est un arbre de preuve
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SNwhich book1
CP
Cdo
SNyou
Vthink
that
SNMary
Vread
VP
CP
V’
V’
VP
xceci est un arbre de preuve
hypothèse
déchargement de l’hypothèse
e
t
e t(e t) t
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règles
A B A
B
« élimination » de
[A]hypothèse
B
A B
Déchargement de l’hypothèse
« introduction » de
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Autre exemple
Nskieur
APgrenoblois
Nskieur grenoblois
Dun
DPun skieur grenoblois
Vaime
VPaime un skieur grenoblois
NPMarie
SMarie aime un skieur grenoblois
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Marie aime un skieur grenoblois
Nskieur
APgrenoblois
Nskieur grenoblois
Dun
DPun skieur grenobloisP.ex(x, ski(x)&gre(x)&P(x))
Vaime
VPaime un skieur grenoblois
NPMarie
SMarie aime un skieur grenoblois
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Déplacement (covert)
DPun skieur grenobloist(race)
Vaime
VPaime un skieur grenoblois
NPMarie
SMarie aime un skieur grenoblois
N AP
ND
P.ex(x, ski(x)&gre(x)&P(x))
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Mais…
Vaime
VPaime un skieur grenoblois
NPMarie
S aime(Marie, xm)Marie aime un skieur grenoblois
N AP
ND
P.ex(x, ski(x)&gre(x)&P(x))
DPun skieur grenobloist(race) -> variable xm
Encore mismatch!
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solution Heim & Kratzer
N AP
ND
P.ex(x, ski(x)&gre(x)&P(x))
Vaime
VPaime un skieur grenoblois
NPMarie
S aime(Marie, xm)Marie aime un skieur grenoblois
DPun skieur grenobloist1(race) -> variable xm
1
Heim & Kratzer: binder
xm. aime(Marie, xm)
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variante
N AP
ND
P.ex(x, ski(x)&gre(x)&P(x))
Vaime
VPaime un skieur grenoblois
NPMarie
S aime(Marie, xm)Marie aime un skieur grenoblois
DPun skieur grenobloist1(race) -> variable xm
S xm. aime(Marie, xm)
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Présentation sous forme de preuve
S xm. aime(Marie, xm)
N AP
ND
P.ex(x, ski(x)&gre(x)&P(x))
Vaime
VPaime un skieur grenoblois
NPMarie
S aime(Marie, xm)Marie aime un skieur grenoblois
DPun skieur grenobloist1(race) -> variable xm
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Vers un système logique
• Cf. déduction naturelle (document)
• mais quel système de déduction naturelle?
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Différences avec la logique classique
• En logique classique :
A, A(A B) |-- A B, mais aussi:
A, A(A B) |-- B (A peut être utilisé deux fois)• Aussi:
A, B |-- B (A utilisé 0 fois!)• Dans un calcul syntaxique, les prémisses ne
sont pas réutilisables
ex : n, n(n s) |-- ns (pas s!)
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Logique classique et logique intuitionnistecf. règles de la déduction naturelle
Règles d’introduction pour:
• Règles d’élimination pour:
Logique classique : rajouter règle d’élimination de la double négation
Logique intuitionniste
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Logique intuitionniste
• Une preuve possède une et une seule conclusion
• Les prémisses = les inputs• La conclusion = l’output• donc une preuve peut être vue comme une
fonction:
A1, …., An B• Il y a un flux d’information dans une direction
privilégiée : des inputs vers l’output
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calcul des séquents
• Gentzen, 1934
• (voir document)
• Logique intuitionniste :– séquents asymétriques : A1, …, An|-- B
• Logique classique :– séquents symétriques : A1, …,An|-- B1,…,Bm
(virgule à gauche : comme un , virgule à droite : comme un )
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représentations géométriques
• Logique intuitionniste :– Les preuves sont des arbres (plus ou moins
enrichis avec des annotations!)
• Logique classique :– Les preuves sont : ?
(des réseaux?)
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Le calcul de Lambek
• Une préfiguration de la logique linéaire…
• Cependant : reste un calcul intuitionniste (les preuves sont représentées par des arbres)
• Sensibilité aux ressources : y compris à l’ordre
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calcul des séquents
Séquent (intuitionniste)
BAAAA ni ,...,,...,, 21
antécédent conséquent
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pour prouver : C ,,,A/B
prouvez :
B
puis prouvez :
A C ,,
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Calcul de Lambek(séquents)
AA
CBACBA
,\,,,,
CABCBA
,,/,,,
BAAB/
,
ABAB\
,
CCAA
, ,, cut
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snsnssnsnsn)//(sn)\(nnnsn /)\(/
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snsnssnsnnnsn /)\(/ sn)//(sn)\(n
sn\nnnnsnsn/ssnssnsn //)\(
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snsnssnsnnnsn /)\(/ sn)//(sn)\(n
sn\nnnnsnsnssnsn //)\( sn/sssnsnssnsn /)\(
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snsnssnsnnnsn /)\(/ sn)//(sn)\(n
sn\nnnnsnsnssnsn //)\( sn/sssnsn sns)/\(snsssnsnsnsn \
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snsnssnsnnnsn /)\(/ sn)//(sn)\(n
sn\nnnnsnsnssnsn //)\( sn/sssnsn sns)/\(snssnsnsn s\snsssnsn
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snsnssnsnnnsn /)\(/ sn)//(sn)\(n
snnnsnsnssnsn n\nsn/s //)\(ssnsn sns)/\(snssnsnsn s\snsssnsn
snnnsnnn /snsnnn