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CAS LX 502

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CAS LX 502 11a. Predicate modification and adjectives – PowerPoint PPT presentation

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Title: 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
?
  • ? ?
  • ?
  • ? ?
  • ? ?
  • ?
  • ?
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