cas lx 502

CAS LX 502

14a. DiscourseRepresentation Theory

10.9

Meaning in discourse

• The formal stuff we have concerned ourselves with so far has primarily been concerned with evaluation of the truth conditions of sentences.

• In connected discourse, there is more going on, we need to take the discourse context into account.

For example

x[delegate(x) arrived(x)]

• ‘A delegate arrived.’

[x[[delegate(x) arrived(x)]]]‘It is not the case that every delegate failed to arrive.’

• A delegate arrived. She registered.

• #It is not the case that every delegate failed to arrive. She registered.

Updating the context

• Somehow A delegate arrived has updated the discourse context to provide an individual referent that can later be referred to by the pronoun She.

• It is not the case that every delegate failed to arrive does not update the context in the same way. It does not introduce a referent.

• Indefinite noun phrases like a delegate can introduce discourse referents.

Lifespan of a referent

• Pati bought an iPodj. Hei brings itj everywhere.• An iPod introduces a discourse referent that the

pronoun it can later refer to.

• #Pat didn’t buy an iPodj. He likes itj though.• If introduced in a negative clause, any discourse

referent there might have been is not available later.

Discourse Representation Theory

• DRT is a formal system to model the progression of meanings and referents in discourse.

• It is a system that keeps track of what referents are introduced and what can refer back to them.

• In the previous case, the negated sentence is the limit of the “reach” of the discourse referent introduced by an iPod. Negation blocks outside reference.

• It is not the case that [Pat bought an iPod].

Donkey science

• DRT is a response to the fairly famous problem with “donkey anaphora” of the following sort:

• If a farmeri owns a donkeyj, hei pets itj.

• It turns out that trying to write the truth conditions for this without the idea of introducing discourse referents is basically impossible.

Problems pre-DRT

• If you steal, you go to jail.

• Steal(you) go-to-jail(you).

• Joan owns a Ferrari.x[Ferrari(x) owns(Joan, x)]

• If Joan owns a Ferrari, she is rich.x[Ferrari(x) owns(Joan, x)] rich(Joan)

Problems pre-DRT

• If Joan owns a Ferrari, she is rich.x[Ferrari(x) owns(Joan, x)] rich(Joan)

• If Joan owns a Ferrari, she drives it.x[Ferrari(x) owns(Joan, x)] drive(Joan, x) ?

• No, that won’t work—x is unbound. Let’s bind it.x[[Ferrari(x) owns(Joan, x)] drive(Joan, x) ]?

• Well, but what does that mean? That’s not right.

Problems pre-DRT

• If Joan owns a Ferrari, she drives it.x[[Ferrari(x) owns(Joan, x)] drive(Joan, x) ]?• “Every Ferrari that Joan owns, she drives”

• That’s more or less right, but how did we get that meaning? Why does a Ferrari sometimes seem like it needs to be interpreted like every Ferrari?

• What is the compositional meaning of a Ferrari?

Discourse Representation Structures

• A DRS represents the discourse by listing the individuals in the “universe” of the DRS and properties known about them.

• Any subsequent sentence will be evaluated against this discourse background, updating the discourse context.

• This is true if there is an x that has those properties.

x

delegate(x)arrived(x)

Discourse Representation Structures

• A delegate arrived.

• She registered.

• Pronouns introduce a condition like y=? (meaning: search for a suitable accessible referent).

• When uttering the sentences in sequence, the second sentence must be merged with the first to yield a new DRS.

x


registered(y)y=?

x y


registered(y)y=x

Complex DRSes

• When constructing a DRS of a negative sentence, a subordinate DRS must be constructed.

• A delegate didn’t arrive

• A sentence of the form if S1 then S2 also requires a subordinate DRS.

• If Joan arrived, Bill arrived.

x


arrived(y)

x y

Joan(x)Bill(y)

arrived(x)

Complex DRSes

• Proper names always introduce referents into the universe of the highest DRS.

• Indefinites like a delegate introduce referents into the DRS containing them.

• If Joan arrived, she met a delegate.

y z

delegate(z)met(y,z)

y=x

x

Joan(x)

arrived(x)

Complex DRSes

• If Joan arrived, she met a delegate. He was tall.

y z

delegate(z)met(y,z)

y=x

x

Joan(x)

arrived(x)w

tall(w)male(w)

w=?

Complex DRSes

• If Joan arrived, she met a delegate. He was tall.

• We can’t assign w to the delegate (referent z).

• The reason is that z is “hidden from view”—it is not accessible to the top-level DRS.

• What referents are accessible are governed by accessibility rules.

y z

delegate(z)met(y,z)

y=x

x w

Joan(x)

tall(w)male(w)

w=?

arrived(x)

Accessibility• If Joan arrived, she met a

delegate. He was tall.

• Suitable referents for an instruction like w=? are any referents in a universe that is either left or out. But never in or right.

• Out but not in:• y and z are not accessible from

the larger DRS. But x and w are accessible from the consequent sub-DRS.

y z

delegate(z)met(y,z)

y=x

x w

Joan(x)

tall(w)male(w)

w=?

arrived(x)

in

out

Accessibility• If a delegate arrived, he was happy.• If he was happy, a delegate arrived.

• Suitable referents for an instruction like w=? are any referents in a universe that is either left or out. But never in or right.

• Left but not right:• x is accessible from the consequent

DRS, but y is not accessible from the antecedent DRS.

y

happy(y)y=x

x

delegate(x) arrived(x)

right

left

y

delegate(y)arrived(y)

x

happy(x) x=?

Sue bought a car. It is fast.

If a boy is hungry, he eats.

If a boy is tired, he doesn’t play.

Pat didn’t buy a textbook.

• We’ve been sort of overlooking the fact that a sentence like Pat didn’t buy a textbook is actually ambiguous.

• It could mean that Pat bought no textbooks. This is basically what our DRSes predict.

• It could also mean that there is a textbook Pat failed to buy.

Unusually wide scope

• A phrase like a textbook is a quantifier, and so we expect that it could undergo QR.

• Assuming that negation is also a quantifier that can undergo QR (we didn’t treat this in our fragment), we expect the normal interaction between two quantifiers:

• A textbook > Not• There is a textbook such that Pat didn’t buy it.

• Not > A textbook• It is not the case that there is a textbook that Pat bought.


• However, QR is usually limited to its own S:

• A fish said [S that Loren likes every book].

• A > every• There is a fish x such that x said that for every

book y, Loren likes y.

• *Every > A• For every book y, there is a fish x such that x said

that for every book y, Loren likes y.


• Tracy drinks tea [S if every student calls].• If > Every

• If, for every student x, x calls, then Tracy drinks tea.

• *Every > If• For every student x, if x calls, then Tracy drinks tea.

• Pat didn’t say [S that Tracy bought every textbook].• Not > Every• *Every > Not


• Every fish said [S that Loren likes a book].

• Tracy drinks tea [S if a student calls].

• With indefinite quantifiers like a book and a student, it seems to be possible to interpret them with widest scope, even when QR can’t normally provide widest scope—and it usually feels like it has a meaning like “a certain.”

Tracy drinks tea if a student calls

• A DRS for the if > a student interpretation would look like this.• If there is a student that

calls, Tracy drinks tea.

• How would we get the other reading?• There is a certain student

such that if s/he calls, Tracy drinks tea.

drinks-tea(x)

x

Tracy(x)

y

student(y) calls(y)

Tracy drinks tea if a student calls

• Essentially what seems to happen is that the indefinite can be treated as a name.

• Making it a name means that it is placed in the universe of the highest DRS.

• This is a specific indefinite. drinks-tea(x)

x y

Tracy(x)student(y)

calls(y)

Every

• Every delegate arrived.

• Our translation of this was:x[delegate(x) arrived(x)]

• That is, being a delegate implies having arrived.

• We can write this asa DRS using the normalrule for writingconditionals. arrived(x)

x

delegate(x)

• The natural interpretation of the sentence on the left is something like: Being a cat implies being constantly on the move. (Generic interpretation).

on-the-move(x)

x

cat(x)

• The second sentence is incompatible with the first on that interpretation, though.

y z

heard-of(y, z)y = speaker

z = ?

on-the-move(x)x

cat(x) on-the-move(x)

y z


z = ?

x

cat(x)

• What makes this “funny” is that we could also write this DRS using a specific indefinite, which can then be referred to using him.

x

cat(x)on-the-move(x)

y z


z = ?

x y z

cat(x)on-the-move(x)heard-of(y, z)y = speaker

z = x

More specific indefinites

• “Last year, I handed in a script, and the studio didn't change one word.

…And the word they didn't change was on page 87.”• (Steve Martin,

hosting the Oscars)

DRT

• Discourse Representation Theory is a system to account for how we track referents through a discourse—how they are introduced, when they can serve as antecedents for pronouns in later sentences.

• The Discourse Representation Structure is a picture of the discourse environment at a given point, updated with each further utterance by merging the information in the new utterance with the information in the discourse environment.

Extra credit (due 4/27)

• 1. Do Saeed, ch. 10, problem 9.• 2. Follow the same instructions for the above problem

with the following two mini-discourses:• Every student took an exami. Iti was 4 pages long.

• If a student writes a paperi, iti is finished at 4am.

• 3. Explain why the following two mini-discourses sound wrong by drawing the final DRS and indicating the problem.• Pat didn’t write a paperi. #Iti was great.

• If Pat writes a paperi, he loses iti. #Iti is under his bed.

• You can treat all of student, take, 4-pages-long, write, finished-at-4am, great, loses, and under-his-bed as predicates.

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