class 14 slides - dspace@mit homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is...
TRANSCRIPT
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Semantics
Image removed for copyright reasons.
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ambiguity:
• British left waffles on Falklands
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ambiguity:
• British left waffles on Falklands• Kicking baby considered to be
healthy
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ambiguity:
• British left waffles on Falklands• Kicking baby considered to be
healthy • Sisters reunited after 18 years
in checkout line at supermarket
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ambiguity:
• British left waffles on Falklands• Kicking baby considered to be
healthy • Sisters reunited after 18 years
in checkout line at supermarket • Dr. Ruth talks about sex
with newspaper editors
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talk [PP about sex] [PP with newspaper editors]
talk [PP about [NP sex with newspaper editors]]
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Another kind of ambiguity
Someone loves everyone.
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"Someone loves everyone":
For each person, X Y Z there is someone who loves them. A B C D E
There is a single X person who loves everyone. A B C D E
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Everyone in this room speaks two languages.
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Everyone in this room speaks two languages.
Two languages are spoken by everyone in this room.
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Not obvious how to make this a structural ambiguity...
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meanings of different kinds of NPs
Mary Ann Walter
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meanings of different kinds of NPs
Mary Ann Walter [is an avid hangglider]
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meanings of different kinds of NPs
The 24.900 TAs [are avid hanggliders]
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meanings of different kinds of NPs
The 24.900 TAs [are avid hanggliders]
{Mary Ann, Andrés, Justin, Pranav, Aly}
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meanings of different kinds of NPs
Every Texan ??
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meanings of different kinds of NPs
Every Texan="Mary Ann Walter, and George Bush, and Molly Ivins, and Lyndon Johnson, and Ross Perot, and Dan Rather, and...."
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meanings of different kinds of NPs
Every Texan [is an avid hangglider]
"Mary Ann Walter, and George Bush, and Molly Ivins, and Lyndon Johnson, and Ross Perot, and Dan Rather, and...." "...are avid hanggliders"
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meanings of different kinds of NPs
"No Texan"=
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meanings of different kinds of NPs
"No Texan"= ???!!@#$?
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meanings of different kinds of NPs
"No Texan"= • null set?
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meanings of different kinds of NPs
"No Texan"= • null set? • a set containing
no Texans?(but which set?)
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quantifiers are weird in other ways:
Andrés is inside, and Andrés is outside.
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quantifiers are weird in other ways:
Andrés is inside, and Andrés is outside.
Several Argentinians are inside, and several Argentinians are outside.
-->some QPs fail the Law of Contradiction
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quantifiers are weird in other ways:
Aly is under 6' tall, or Aly is over 5' tall.
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quantifiers are weird in other ways:
Aly is under 6' tall, or Aly is over 5' tall.
All Californians are under 6' tall, or all Californians are over 5' tall.
-->some QPs fail the Law of the Excluded Middle
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Quantifier MeaningOkay, so
No Texans Several Argentinians All Californians Most Americans...
don't refer to sets of people. So what do they mean?
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A little quick set theory
Image removed for copyright reasons.
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A little quick set theory
ΠΠΠΠ A C ΦΦΦΦB D E
F
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A little quick set theory
ΠΠΠΠ A C ΦΦΦΦB D E
F
{D, F}=the intersection of ΠΠΠΠ and ΦΦΦΦ (ΠΠΠΠ ∩ ΦΦΦΦ)
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A little quick set theory
ΠΠΠΠ A C ΦΦΦΦB D E
F
{D, F}=the intersection of ΠΠΠΠ and ΦΦΦΦ (ΠΠΠΠ ∩ ΦΦΦΦ) {A, B, C, D, E, F}=the union of of ΠΠΠΠ and ΦΦΦΦ (ΠΠΠΠ ∪ ΦΦΦΦ)
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A little quick set theory
ΠΠΠΠ A C ΦΦΦΦB D E
F
{D, F}=the intersection of ΠΠΠΠ and ΦΦΦΦ (ΠΠΠΠ ∩ ΦΦΦΦ) {A, B, C, D, E, F}=the union of of ΠΠΠΠ and ΦΦΦΦ (ΠΠΠΠ ∪ ΦΦΦΦ) {A, B, D} is a subset of ΠΠΠΠ ({A, B, D}¤ ΠΠΠΠ)
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Quantifier Meaninga popular answer:
All Americans eat junk food.
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Quantifier Meaninga popular answer:
All Americans eat junk food
denotes set of Americans denotes set of junk-food-eaters
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Quantifier Meaninga popular answer:
All Americans eat junk food
denotes set of Americans denotes set of junk-food-eaters
all:set #1 is a subset of set #2
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Quantifier Meaning
Some Americans eat junk food
denotes set of Americans denotes set of junk-food-eaters
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Quantifier Meaning
Some Americans eat junk food
denotes set of Americans denotes set of junk-food-eaters
some : the intersection of set #1 and set #2 is nonempty
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Quantifier Meaning
No Americans eat nattoo
denotes set of Americans denotes set of nattooeaters
no: the intersection of set #1 and set #2 is empty
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Quantifier Meaning
all:set #1 is a subset of set #2 some : the intersection of set #1 and
set #2 is nonempty no: the intersection of set #1 and set
#2 is empty three: the intersection of set #1 and
set #2 has cardinality three.
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Quantifier Meaning
Natural language quantifiers are conservative, which means that you can always replace "set #2" with "the intersection of set #1 and set #2", and get the same meaning.
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Quantifier Meaning: conservativity
All opera singers smoke
{opera singers} ¤ {smokers}
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Quantifier Meaning: conservativity
All opera singers smoke
{opera singers} ¤ {smokers}
All opera singers are opera singers who smoke
{opera singers} ¤ { {smokers}∩{opera singers} }
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Quantifier Meaning: conservativity
This isn't trivial. It's easy to imagine quantifiers which wouldn't be conservative:
glorp: the union of set #1 and set #2 has cardinality three.
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Quantifier Meaning: conservativity
This isn't trivial. It's easy to imagine quantifiers which wouldn't be conservative:
glorp: the union of set #1 and set #2 has cardinality three.
"Glorp circles are red"
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Quantifier Meaning: conservativity
This isn't trivial. It's easy to imagine quantifiers which wouldn't be conservative:
glorp: the union of set #1 and set #2 has cardinality three.
"Glorp circles are red"≠ "Glorp circles are red circles"
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Quantifier Meaning
All [Filipinos] [love balut]=
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Quantifier Meaning
All [Filipinos] [love balut]=
{Filipinos} is a subset of {people who love balut}
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Quantifier Meaning
All [Filipinos] [love balut]=
{Filipinos} is a subset of{people who love balut} (={people such that they love balut})
(replace the quantifier with a pronoun)
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Quantifier Meaning
Balut disgusts [all [Americans]]
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Quantifier Meaning
Balut disgusts [all [Americans]]
{Americans} is a subset of {people whom balut disgusts}
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Quantifier Meaning
Balut disgusts [all [Americans]]
{Americans} is a subset of {people whom balut disgusts} (={people such that balut disgusts them})
again, quantifier replaced w/pronoun
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Quantifier Scope Ambiguity
[Some child] loves [every puppy]
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Quantifier Scope Ambiguity
[Some child] loves [every puppy]
• interpreting every first: {puppies} is a subset of {things such that some child loves them}
![Page 54: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/54.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]
• interpreting every first:{puppies} is a subset of{things such that some child loves them}
now how do we interpret this part?
![Page 55: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/55.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]
• interpreting every first: {puppies} is a subset of {things such that:
the intersection of {children} with {people such that they love them} is nonempty}
![Page 56: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/56.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]
• translating this from Semantics into English: every member of {puppies} is such that:
the intersection of {children} with {people such that they love them} is nonempty
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Quantifier Scope Ambiguity
[Some child] loves [every puppy]
• translating this from Semantics into English: every member of {puppies} is such that: there is some child that loves it.
![Page 58: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/58.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]
every member of {puppies} is such that: there is some child that loves it.
Images of child and dog removed for copyright reasons.
![Page 59: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/59.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]
We just saw how this gets interpreted if we interpret every puppy first. How about if we interpret some child first?
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Quantifier Scope Ambiguity
[Some child] loves [every puppy]
The intersection of {children} and {people such that they love every puppy} is nonempty.
![Page 61: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/61.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]
The intersection of {children} and {people such that they love every puppy} is
next we interpret this... nonempty.
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Quantifier Scope Ambiguity
[Some child] loves [every puppy]
The intersection of {children} and {people such that: {puppies} is a subset of {things such thatthey love them}} is nonempty.
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Quantifier Scope Ambiguity
[Some child] loves [every puppy]
The intersection of {children} and {people such that: {puppies} is a subset of {things such that they love them}} is nonempty. (...now to translate this
back into English.....)
![Page 64: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/64.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]
There is at least one child such that:
{puppies} is a subset of {things such that they love them}}
![Page 65: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/65.jpg)
Quantifier Scope Ambiguity
[Some child] loves [every puppy]There is at least one child such that: all puppies are loved by them.
Images of child and dog removed for copyright reasons.
![Page 66: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/66.jpg)
Quantifier Scope Ambiguity[Some child] loves [every puppy]There is at least one child such that: all puppies are loved by them.
every puppy is such that: there is some child that loves it.
![Page 67: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/67.jpg)
Quantifier Scope Ambiguity[Some child] loves [every puppy]There is at least one child such that: all puppies are loved by them.
every puppy is such that: there is some child that loves it.
-->just saw how to get this ambiguity to follow from different orders of quantifier interpretation.
![Page 68: class 14 slides - DSpace@MIT Homedspace.mit.edu/bitstream/handle/1721.1/80262/24-900...all:set #1 is a subset of set #2 some : the intersection of set #1 and set #2 is nonempty no:](https://reader036.vdocuments.us/reader036/viewer/2022070110/6046bf0be63f0422284e8181/html5/thumbnails/68.jpg)
Quantifier Scope Ambiguity
IP So why is this tree ambiguous?
NP I'
some child I VP -s
V'
V NP love
every puppy
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Quantifier Scope Ambiguity
IP Do we just get to freely choose the order in which
NP I' we interpret quantifiers?
some child I VP -s
V'
V NP love
every puppy
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Quantifier Scope Ambiguity
IP Nope. Lots of evidence:
NP I' Quantifier Raising
some child I -s
V'
V love
every puppy
VP
NP
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Binding Theory
Susan likes herself.
Susan likes her.
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Binding Theory
Susana likes herselfa.
Susana likes herb.
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Binding Theory
Susana likes herselfa.
Susana likes herb.
*Susana likes herselfb.
*Susana likes hera.
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Binding Theory
Susana likes herselfa.
Susana likes herb. pronouns cannot corefer with anything
*Susana likes herselfb. in the sentence.
*Susana likes hera.
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Binding Theoryanaphors must
Susana likes herselfa. corefer with something.
Susana likes herb. pronouns cannot corefer with anything
likes herselfb. in the sentence.
likes hera.
*Susana
*Susana
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Binding Theory
anaphors must corefer with something?
Susana likes herselfa.*Susana likes herselfb.
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Binding Theory
anaphors must corefer with something?
Susana likes herselfa.*Susana likes herselfb.
*Susana's father likes herselfa.
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Binding TheoryIP IP
NP I' NP I'
Susan I VP DP N' I VP [pres] NP [pres]
V' D' N V' Susan father
V NP D V NP likes 's likes
herself herself
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Binding TheoryIP IP
NP I' NP I'
Susan I VP DP N' I VP [pres] NP [pres]
V' D' N V' Susan
V NP likes
herself
father D V NP 's likes
herself
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Binding TheoryIP c-command: α c-commands β
if all the nodes dominating α NP I' dominate β.
Susan I [pres]
V'
V likes
herself
VP
NP
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Binding TheoryIP c-command: α c-commands β
if all the nodes dominating α NP I' dominate β.
Susan I [pres]
VP only node
V'
V likes
herself
NP
dominating the NP Susan also dominates the NP herself.
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Binding TheoryIP c-command: α c-commands β
if all the nodes dominating α NP I' dominate β.
Susan I [pres]
VP
V' -->Susan c-commands herself.V
likes herself
NP
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Binding TheoryIP
NP I'
DP N' I [pres]
NP father
Susan D V NP 's likes
herself
VP
D' N V'
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Binding TheoryIP
NP I' all dominate Susan; not all dominate herself
DP N' I VP [pres]
NP D' N V' father
Susan D V NP 's likes
herself
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Binding TheoryIP
NP I' -->Susan doesn't c-command herself.
DP N' I VP [pres]
NP D' N V' father
Susan D V NP 's likes
herself
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Binding Theory
anaphors (words like herself, myself, etc.) must be c-commanded by something that corefers with them.
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Binding Theory
anaphors (words like herself, myself, etc.) must be c-commanded by something that corefers with them.
α binds β if α c-commands and corefers with β.
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Binding Theory
anaphors must be bound.
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Binding Theory
anaphors must be bound.
anaphors include: reflexives (herself) reciprocals (each other)
[John and Bill] like each other * [John and Bill]'s father likes each other
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Binding Theory
anaphors must be bound. pronouns must be free (=not bound)
Susana likes herselfa. * Susana's father likes herselfa. * Susana likes hera.
Susana's father likes hera.
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Binding Theory
Susana likes herselfa.
I told Susana about herselfa.
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Binding Theory
Susana likes herselfa.
I told Susana about herselfa.
*Herselfa likes Susana.
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Binding Theory
Susana likes herselfa.
*Susana thinks I like herselfa.
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Binding Theory
Susana likes herselfa.
*Susana thinks I like herselfa.
Principle A: anaphors must be bound...within IP.
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Binding Theory
*Susana likes hera.
Susana thinks I like hera.
Principle A: anaphors must be bound...within IP.Principle B: pronouns must be free...within IP.
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Binding Theory
*Shea likes Susana.
Hera father likes Susana.
Principle A: anaphors must be bound within IP.Principle B: pronouns must be free within IP.
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Binding Theory
*Shea likes Susana.
Hera father likes Susana.
Principle A: anaphors must be bound within IP. Principle B: pronouns (and names?) must be free within IP.
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Binding Theory
Susana thinks I like hera.*Shea thinks I like Susana.
Principle A: anaphors must be bound within IP. Principle B: pronouns (and names?) must be free within IP.
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Binding Theory
Susana thinks I like hera.*Shea thinks I like Susana.
Principle A: anaphors must be bound within IP. Principle B: pronouns (and names?) must be free within IP.Principle C: "R-expressions" must be free.
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Binding Theory
[While she was eating], Susan read a book.
*She read a book while Susan was eating.