CAS LX 502 14a. Discourse Representation Theory 10.9.
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Transcript of CAS LX 502 14a. Discourse Representation Theory 10.9.
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
delegate(x)arrived(x)
registered(y)y=?
x y
delegate(x)arrived(x)
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
delegate(x)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.
Unusually wide scope
• 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.
Unusually wide scope
• 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
Unusually wide scope
• 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
heard-of(y, z)y = speaker
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
heard-of(y, z)y = speaker
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.