Title: CAS LX 502
1CAS LX 502
- 11a. Predicate modificationand adjectives
2Is 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.
3Bond 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)
4Bond 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
5Bond 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
6Bond 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
7Bond 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
8Bond 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
9Bond 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
10Bond 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
11Every 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
12Nemo 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.
13Nemo 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.
14Nemo 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
15Nemo 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
16Nemo 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
17What 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.
18Equative 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
19Nemo 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.
20Nemo 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
21Nemo 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
22Nemo 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
23Predicate 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).
24Predicate 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)
25Nemo 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
26Nemo 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
28Quantifier 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
29The 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.
30A 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)
31The 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
32Relative clause transformation
NP
Det
NC
S
NC
S?
?
NP
that
S?
Det
NC
S
i
ti
33?