CAS LX 502

11a. Predicate modificationand adjectives

Is hungry

• As a starting point, we’ve 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, <e,t>.

• In is hungry, the verb is is not contributing any meaning, it’s just there to link up the subject and the adjective.

Bond is hungry

• Let’s tweak our syntax so that is hungry is comprised of is and hungry, and let’s say that is has no semantic value, that it is meaningless.

• VP Vbe Adj

• Vbe is• Adj hungry, happy, tall• [Vbe]M,g = —• [hungry]M,g = x [ x F(hungry) ]

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 has only one daughter with a semantic value, , then []M,g = []M,g

S

NP VP

Vbe

is

NP

Bond

Adj

hungry

Bond is hungry

• Pass-UpIf a node has only one daughter with a semantic value, , then []M,g = []M,g

S

NP VP

Vbe

is

NP

Bond

Adj

hungry

x [ x F(hungry) ]<e,t>

Bond is hungry

• Pass-UpIf a node has only one daughter with a semantic value, , then []M,g = []M,g

S

NP VP

Vbe

is

NP

Bond

Adj

hungry

x [ x F(hungry) ]<e,t>

x [ x F(hungry) ]<e,t>

Bond is hungry

• Pass-UpIf a node has only one daughter with a semantic value, , then []M,g = []M,g

S

NP VP

Vbe

is

NP

Bond

Adj

hungry

x [ x F(hungry) ]<e,t>

x [ x F(hungry) ]<e,t>

x [ x F(hungry) ]<e,t>

Bond is hungry

• Pass-UpIf a node has only one daughter with a semantic value, , then []M,g = []M,g

S

NP VP

Vbe

is

NP

Bond

Adj

hungry

x [ x F(hungry) ]<e,t>

F(Bond) ]<e>

Bond is hungry

• Pass-UpIf a node has only one daughter with a semantic value, , then []M,g = []M,g

• Functional application[ ]M,g =[]M,g ( []M,g )or []M,g ( []M,g ) whichever is defined

S

NP VP

Vbe

is

NP

Bond

Adj

hungry

x [ x F(hungry) ]<e,t>

F(Bond) ]<e>

Bond is hungry

• Functional application[ ]M,g =[]M,g ( []M,g )or []M,g ( []M,g ) whichever is defined

• [S]M,g = [VP]M,g ( [NP]M,g )= x [ x F(hungry) ] ( [NP]M,g )= x [ x F(hungry) ] ( F(Bond) )= F(Bond) F(hungry)

S

NP VP

Vbe

is

NP

Bond

Adj

hungry

x [ x F(hungry) ]<e,t>

F(Bond) ]<e>

Every hungry fish is happy

• By separating is from hungry, we’ve 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

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 means that there is an x that for which both and hold.

• Every means that for every x, being implies also being .

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 doesn’t really feel like that. Also, notice that every cannot be used here:• *Nemo is every happy fish.

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, let’s 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 = —

Nemo is a fish

• There’s nothing new or fancy going on here, just more use of Pass-Up.

• [fish]M,g = x [ x F(fish) ]

• [DETdummy a]M,g = —

• [is]M,g = —

S

NP VP

Vbe

is

NP

Nemo

NPpred

fish

Detdummy

a

NC

x [ x F(fish) ]<e,t>

Nemo is a fish

• Then, as before:

• [S]M,g = [VP]M,g ( [NP]M,g )= x [ x F(fish) ] ( [NP]M,g )= x [ x F(fish) ] ( F(Nemo) )= F(Nemo) F(fish)

S

NP VP

Vbe

is

NP

Nemo

NPpred

fish

Detdummy

a

NC

x [ x F(fish) ]<e,t>

x [ x F(fish) ]<e,t>

F(Nemo)<e>

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 we’ll call predicative. The “equals” kind of is we’ll call equative.

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 and to NPs):

• [is]M,g = [ [ []M,g = []M,g ] ]

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.

Nemo is a happy fish

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

S

NP VP

Vbe

is

NP

Nemo

NPpred

fish

Detdummy

a NC

x [ x F(fish) ]<e,t>

NC

Adj

happy

x [ x F(happy) ]<e,t>

?

Nemo is a happy fish

• What type should happy fish be?• Seems like it should be

the same as fish.

• A property (a predicate), true of individuals (<e,t>), that are happy and fish.

• Nemo is happy and Nemo is a fish.

S

NP VP

Vbe

is

NP

Nemo

NPpred

fish

Detdummy

a NC

x [ x F(fish) ]<e,t>

NC

Adj

happy

x [ x F(happy) ]<e,t>

?<e,t>

Nemo is a happy fish

• 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) ]

S

NP VP

Vbe

is

NP

Nemo

NPpred

fish

Detdummy

a NC

x [ x F(fish) ]<e,t>

NC

Adj

happy

x [ x F(happy) ]<e,t>

?<e,t>

Predicate modification

• To make the structure interpretable and to accomplish the desired meaning, we add a third interpretation rule:

• Predicate modification[ ]M,g = z [ []M,g(z) []M,g(z) ]where and are predicates (type <e,t>).

Predicate modification• Predicate modification

[ ]M,g = z [ []M,g(z) []M,g(z) ]where and are predicates (type <e,t>).

• For [happy fish]M,g, will be happy, will be fish.• [happy]M,g = x [ x F(happy) ]• [fish]M,g = x [ x F(fish) ]• [happy fish]M,g

= z [ [happy]M,g(z) [fish]M,g(z) ]= z [ x [ x F(happy) ](z) [fish]M,g(z) ]= z [ z F(happy) [fish]M,g(z) ]= z [ z F(happy) x [ x F(fish) ](z) ]= z [ z F(happy) z F(fish) ]

Nemo is ahappy fish

• 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, so[NC]M,g is passed upall the way to [VP]M,g.

S

NP VP

Vbe

is

NP

Nemo

NPpred

fish

Detdummy

a NC

x [ x F(fish) ]<e,t>

NC

Adj

happy x [ x F(happy) ]<e,t>

z [ z F(happy) z F(fish) ] <e,t>

Nemo is ahappy fish

• [S]M,g = [VP]M,g ( [NP]M,g )= z [ z F(happy) z F(fish) ] ( [NP]M,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.

S

NP VP

Vbe

is

NP

Nemo

NPpred

fish

Detdummy

a NC

NC

Adj

happy

z [ z F(happy) z F(fish) ] <e,t>

F(Nemo)<e>

(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

Vt likes, hates

Adj boring, hungry

Neg it is not the case that NC book, fish, man, woman

Detdummy a Vbe is

[Pavarotti]M,g = F(Pavarotti) (any NP)

[boring]M,g = x [ x F(boring) ] (any NC or Adj or Vi)

[likes]M,g = y [ x [ <x,y> F(likes) ] ] (any Vt)

[and]M,g = y [ x [ x y ] ] (analogous for or)

[it is not the case that]M,g = x [ x ]

[every]M,g = P [ Q [ xU [P(x) Q(x)] ] ]

[a]M,g = P [ Q [ xU [P(x) Q(x)] ] ]

[i]M,g = g(i) [is]M,g = —

[i]M,g = S [x [ [S]M,g[i/x] ] ] [DETdummy a]M,g = —

Pass-UpIf a node has only one daughter with a semantic value, , then []M,g = []M,g

Functional application [ ]M,g = []M,g ( []M,g )

or []M,g ( []M,g )

Quantifier Raising[S X NP Y ][S NP [S i [S X ti Y ]]]

Predicate modification[ ]M,g = z [ []M,g(z) []M,g(z) ]where and are predicates

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 doesn’t seem to rely on the value of the sentence:

• Every means for each x, if is true of x, is also true of x.

• The is just an individual, one of which is true, with the presupposition that there is only one individual of which is true.

A unique fish

• However, rather than try to incorporate presuppositions into F3, we’ll 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)

• [the]M,g =P [ Q [ xU [P(x) y[P(y)x=y] Q(x)] ] ]

• [a]M,g =P [ Q [ xU [P(x) Q(x)] ] ]

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 transformation:[S X Det NC Y ][NP Det [Nc NC [S that [S i [S X ti Y ] ] ] ] ]

Relative clause transformation

• [that]M,g = —

S

… ti …

S

S

i

Det

NC

… NP …

Det NC

S

that

NC

NP