CAS LX 502

1
CAS LX 502

• 11a. Predicate modificationand adjectives

2
Is hungry

• As a starting point, weve been considering is
  hungry to be an intransitive verb.
• Really, though, is is the verb, hungry is an
  adjective.
• An individual can either be hungry or not hungry.
  That is, hungry is either true or false of an
  individual. Hungry is a function from individuals
  to truth values, lte,tgt.
• In is hungry, the verb is is not contributing any
  meaning, its just there to link up the subject
  and the adjective.

3
Bond is hungry

• Lets tweak our syntax so that is hungry is
  comprised of is and hungry, and lets say that is
  has no semantic value, that it is meaningless.
• VP ? Vbe Adj
• Vbe ? is
• Adj ? hungry, happy, tall
• VbeM,g
• hungryM,g ? x x ? F(hungry)

4
Bond is hungry

• To interpret this we want is to be ignored. To be
  precise, we can slightly modify Pass-Up so that
  it applies to this case.
• Pass-UpIf a node b has only one daughter with a
  semantic value, a, then bM,g aM,g

S
NP
VP
Vbe
NP
Adj
is
Bond
hungry
5
Bond is hungry

• Pass-UpIf a node b has only one daughter with a
  semantic value, a, then bM,g aM,g

S
NP
VP
Vbe
NP
Adj
is
Bond
hungry
? x x ? F(hungry) lte,tgt
6
Bond is hungry
? x x ? F(hungry) lte,tgt

• Pass-UpIf a node b has only one daughter with a
  semantic value, a, then bM,g aM,g

S
NP
VP
Vbe
NP
Adj
is
Bond
hungry
? x x ? F(hungry) lte,tgt
7
Bond is hungry
? x x ? F(hungry) lte,tgt

• Pass-UpIf a node b has only one daughter with a
  semantic value, a, then bM,g aM,g

S
NP
VP
Vbe
NP
Adj
is
Bond
hungry
? x x ? F(hungry) lte,tgt
? x x ? F(hungry) lte,tgt
8
Bond is hungry
? x x ? F(hungry) lte,tgt

• Pass-UpIf a node b has only one daughter with a
  semantic value, a, then bM,g aM,g

S
NP
VP
Vbe
NP
Adj
is
Bond
hungry
F(Bond) ltegt
9
Bond is hungry
? x x ? F(hungry) lte,tgt
F(Bond) ltegt

• Pass-UpIf a node b has only one daughter with a
  semantic value, a, then bM,g aM,g
• Functional applicationg a b M,g bM,g (
  aM,g )or aM,g ( bM,g ) whichever is
  defined

S
NP
VP
Vbe
NP
Adj
is
Bond
hungry
10
Bond is hungry
? x x ? F(hungry) lte,tgt
F(Bond) ltegt
S

• Functional applicationg a b M,g bM,g (
  aM,g )or aM,g ( bM,g ) whichever is
  defined
• SM,g VPM,g ( NPM,g ) ? x x ?
  F(hungry) ( NPM,g ) ? x x ? F(hungry) (
  F(Bond) ) F(Bond) ? F(hungry)

NP
VP
Vbe
NP
Adj
is
Bond
hungry
11
Every hungry fish is happy

• By separating is from hungry, weve isolated a
  category of adjectives, which also appear in noun
  phrases modifying a common noun, as in every
  hungry fish.
• Now that we have adjectives, we can turn a common
  noun like fish into a more descriptive common
  noun like hungry fish inching closer to actual
  English.
• NC ? Adj NC

12
Nemo is a fish

• One more detour before we continue What is the
  contribution of a in Nemo is a fish?
• We have a listed as a quantifier, meaning
  essentially the same as some, e.g.,
• A fish likes every book.
• Some fish likes every book.
• A a b means that there is an x that for which
  both a and b hold.
• Every a b means that for every x, being a implies
  also being b.

13
Nemo is a fish

• But does Nemo is a fish really mean There is an
  x that is a fish, and Nemo is that x?
• It doesnt really feel like that. Also, notice
  that every cannot be used here
• Nemo is every happy fish.

14
Nemo is a fish

• What it seems like intuitively is that a is not
  adding anything to the meaning either. That, like
  is, a is just meaningless, passing along the
  meaning of the common noun.
• So, lets allow for that by building in a dummy
  determiner that has no meaning and shows up only
  when the verb is is.
• VP ? Vbe NPpred
• NPpred ? Detdummy NC
• Detdummy ? a
• DETdummy a M,g

15
Nemo is a fish

• Theres nothing new or fancy going on here, just
  more use of Pass-Up.
• fishM,g ? x x ? F(fish)
• DETdummy aM,g
• isM,g

S
NP
VP
Vbe
NP
NPpred
is
Nemo
Detdummy
NC
fish
a
? x x ? F(fish) lte,tgt
16
Nemo is a fish
? x x ? F(fish) lte,tgt
F(Nemo) ltegt
S

• Then, as before
• SM,g VPM,g ( NPM,g ) ? x x ? F(fish)
  ( NPM,g ) ? x x ? F(fish) ( F(Nemo) )
  F(Nemo) ? F(fish)

NP
VP
Vbe
NP
NPpred
is
Nemo
Detdummy
NC
fish
a
? x x ? F(fish) lte,tgt
17
What the meaning of is is

• Is is always meaningless?
• It seems to be in Nemo is a fish.
• But what about in Nemo is the President? Or A
  hungry fish is a happy fish?
• The meaningless kind of is well call
  predicative. The equals kind of is well call
  equative.

18
Equative be

• The equative is is kind of like a conjunction
  that means equals and seems to be able to
  equate any two NPs. We might give the rule as
  (perhaps limiting a and b to NPs)
• isM,g ?b ?a aM,g bM,g

19
Nemo is a happy fish

• We added a rule to allow for adjectives to attach
  to common nouns
• NC ? Adj NC
• So, we should be able to draw a structure for
  Nemo is a happy fish.

20
Nemo is a happy fish
S
?
NP
VP

• However, when we try to work out the truth
  conditions, we run into a problem.

Vbe
NP
NPpred
is
Nemo
Detdummy
NC
a
NC
Adj
fish
happy
? x x ? F(happy) lte,tgt
? x x ? F(fish) lte,tgt
21
Nemo is a happy fish
S
?lte,tgt

• What type should happy fish be?
• Seems like it should be the same as fish.
• A property (a predicate), true of individuals
  (lte,tgt), that are happy and fish.
• Nemo is happy and Nemo is a fish.

NP
VP
Vbe
NP
NPpred
is
Nemo
Detdummy
NC
a
NC
Adj
fish
happy
? x x ? F(happy) lte,tgt
? x x ? F(fish) lte,tgt
22
Nemo is a happy fish
S
?lte,tgt

• We want something that,given an individual z,is
  trueif happy is true of zand fish is true of z.
• ? z z ? F(happy) ? z ? F(fish)

NP
VP
Vbe
NP
NPpred
is
Nemo
Detdummy
NC
a
NC
Adj
fish
happy
? x x ? F(happy) lte,tgt
? x x ? F(fish) lte,tgt
23
Predicate modification

• To make the structure interpretable and to
  accomplish the desired meaning, we add a third
  interpretation rule
• Predicate modificationa bM,g ? z aM,g(z)
  ? bM,g(z) where a and b are predicates (type
  lte,tgt).

24
Predicate modification

• Predicate modificationa bM,g ? z aM,g(z)
  ? bM,g(z) where a and b are predicates (type
  lte,tgt).
• For happy fishM,g, a will be happy, b will be
  fish.
• happyM,g ? x x ? F(happy)
• fishM,g ? x x ? F(fish)
• happy fishM,g ? z happyM,g(z) ?
  fishM,g(z) ? z ? x x ? F(happy) (z) ?
  fishM,g(z) ? z z ? F(happy) ?
  fishM,g(z) ? z z ? F(happy) ? ? x x ?
  F(fish) (z) ? z z ? F(happy) ? z ? F(fish)
  

25
Nemo is ahappy fish
? z z ? F(happy) ? z ? F(fish) lte,tgt
S

• Now that we have a semantic value for the whole
  NC, the rest proceeds as in Nemo is a fish from
  before.
• Is and a have nosemantic value, soNCM,g is
  passed upall the way to VPM,g.

NP
VP
Vbe
NP
NPpred
is
Nemo
Detdummy
NC
a
NC
Adj
fish
happy
? x x ? F(happy) lte,tgt
? x x ? F(fish) lte,tgt
26
Nemo is ahappy fish
? z z ? F(happy) ? z ? F(fish) lte,tgt
F(Nemo) ltegt
S
NP
VP
Vbe
NP
NPpred
is
Nemo
Detdummy
NC

• SM,g VPM,g ( NPM,g ) ? z z ? F(happy)
  ? z ? F(fish) ( NPM,g ) ? z z ? F(happy)
  ? z ? F(fish) ( F(Nemo) ) F(Nemo) ? F(happy)
  ? F(Nemo) ? F(fish)
• Nemo is happy and Nemo is a fish.

a
NC
Adj
fish
happy
27
(F3)
S ? NP VP VP ? Vt NP
S ? S ConjP VP ? Vi
ConjP ? Conj S NP ? Det NC
S ? Neg S NP ? NP
VP ? Vbe NPpred NC ? Adj NC
NPpred ? Detdummy NC
Det ? the, a, every NP ? Pavarotti, Loren, Bond, Nemo, Dory, Blinky, Semantics, The Last Juror, hen, shen, itn, himn, hern, himselfn, herselfn, itselfn.
Conj ? and, or NP ? Pavarotti, Loren, Bond, Nemo, Dory, Blinky, Semantics, The Last Juror, hen, shen, itn, himn, hern, himselfn, herselfn, itselfn.
Vt ? likes, hates NP ? Pavarotti, Loren, Bond, Nemo, Dory, Blinky, Semantics, The Last Juror, hen, shen, itn, himn, hern, himselfn, herselfn, itselfn.
Adj ? boring, hungry NP ? Pavarotti, Loren, Bond, Nemo, Dory, Blinky, Semantics, The Last Juror, hen, shen, itn, himn, hern, himselfn, herselfn, itselfn.
Neg ? it is not the case that NC ? book, fish, man, woman
Detdummy ? a Vbe ? is
28
Quantifier RaisingS X NP Y ?S NP S? i S X ti Y Predicate modificationa bM,g ?z aM,g(z) ? bM,g(z) where a and b are predicates
Pass-UpIf a node b has only one daughter with a semantic value, a, then bM,g aM,g Functional application g a b M,g bM,g ( aM,g ) or aM,g ( bM,g )
PavarottiM,g F(Pavarotti) (any NP) PavarottiM,g F(Pavarotti) (any NP)
boringM,g ? x x ? F(boring) (any NC or Adj or Vi) boringM,g ? x x ? F(boring) (any NC or Adj or Vi)
likesM,g ? y ? x ltx,ygt ? F(likes) (any Vt) likesM,g ? y ? x ltx,ygt ? F(likes) (any Vt)
andM,g ? y ? x x ? y (analogous for or) andM,g ? y ? x x ? y (analogous for or)
it is not the case thatM,g ? x ?x it is not the case thatM,g ? x ?x
everyM,g ?P ?Q ?x?U P(x) ? Q(x) everyM,g ?P ?Q ?x?U P(x) ? Q(x)
aM,g ?P ?Q ?x?U P(x) ? Q(x) aM,g ?P ?Q ?x?U P(x) ? Q(x)
?iM,g g(i) isM,g
iM,g ?S ?x SM,gi/x DETdummy aM,g
29
The boring fish

• There are two more things to add to our system
  before we call it complete enough for this
  semester.
• One is to add an interpretation for the (which
  our syntax can generate), as in the boring fish.
• The is a Det but it is different from every It
  doesnt seem to rely on the value of the
  sentence
• Every a b means for each x, if a is true of x, b
  is also true of x.
• The a is just an individual, one of which a is
  true, with the presupposition that there is only
  one individual of which a is true.

30
A unique fish

• However, rather than try to incorporate
  presuppositions into F3, well instead define the
  to be a quantifier like every or a except meaning
  a unique.
• (This means not presupposing existence and
  uniqueness, but rather asserting it)
• theM,g ?P ?Q ?x?U P(x) ? ?yP(y)?xy ?
  Q(x)
• aM,g ?P ?Q ?x?U P(x) ? Q(x)

31
The fish that Bond likes

• The last thing to incorporate is the relative
  clause.
• Idea suppose we start with Bond likes the fish
  and we transform this S into an NP (the fish that
  Bond likes) by doing something similar to QR.
• Relative clause transformationS X Det NC Y
  ?NP Det Nc NC S? that S? i S X ti Y
  

32
Relative clause transformation
NP
Det
NC
S
NC
S?
?
NP
that
S?
Det
NC
S
i
ti

• thatM,g

33
?

• ? ?
• ?
• ? ?
• ? ?
• ?
• ?