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The pragmatics of questions and answers
Christopher Potts
UMass Amherst Linguistics
CMPSCI 585, November 6, 2007
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Background Pragbot
This lecture
1 A brief, semi-historial overview of linguistic pragmatics
2 A few notes on the SUBTLE project
3 Some illustrative examples
4 The partition semantics for questions
5 A decision-theoretic approach
6 Research challenges
Useful follow-up reading: Chapters 23 and 24 of Jurafsky andMartin (chapters 18 and 19 of the 1st edition)
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Background Pragbot
The merest sketch
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Background Pragbot
The merest sketch
“So here is the miracle: from a merest,sketchiest squiggle of lines, you and I con-verge to find adumbration of a coherentscene”
“The problem of utterance interpretationis not dissimilar to this visual miracle. Anutterance is not, as it were, a verdicalmodel or ‘snapshot’ of the scene it de-
scribes”
—Levinson (2000)
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Background Pragbot
The birth of Gricean pragmatics
In the early 1960s, Chomsky showed us howto give compact, general specifications of
natural language syntax.
In the late 1960s, philosopher and linguistH. Paul Grice had the inspired idea to dothe same for (rational) social interactions.
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Background Pragbot
Rules and maxims
Rules
S ⇒ NP VPNP ⇒ N|PN
N ⇒ hippo | · · ·
VP ⇒ Vs SVP ⇒ Vtrans NPVs ⇒ realize | · · ·
Maxims
Quality Above all, be truthful!Relevance And be relevant!Quantity Within those bounds, be
as informative as you can!Manner And do it as clearly andconcisely as possible!
Syntactic rules are like physical laws.
Breaking them should lead to nonsense (or falsification).
Pragmatic rules (maxims) are like laws of the land.
Breaking them can have noteworthy consequences.
B k d P b
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Background Pragbot
Pragmatic pressuresMaxims
Quality Above all, be truthful!
Relevance And be relevant!
Quantity Within those bounds,be as informative as you can!
Manner And do it as clearlyand concisely as possible!
B k d P b t
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Background Pragbot
“Then a miracle occurs”
The maxims do not yield
easily to a treatment inthe usual terms of seman-tic theory. One can usu-ally be precise up to a
point, but then . . .
Background Pragbot
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Background Pragbot
“Then a miracle occurs”
The maxims do not yield
easily to a treatment inthe usual terms of seman-tic theory. One can usu-ally be precise up to a
point, but then . . .
Background Pragbot
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Background Pragbot
The probability of formalizing the maxims
Some are skeptical:
• Beaver (2001:29) calls formalization in this area“notoriously problematic”.
• Bach (1999) is more decisive, offering various reasons why“it seems futile for linguists to seek a formal pragmatics”.
• Devitt and Sterelny (1987:§7.4) strike a similar chord.
It’s a harsh verdict. Maxims (at least one) are the main enginebehind all pragmatic theories.
Background Pragbot
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Background Pragbot
A probable breakthrough
Things are looking up.Researchers are making significant progress with
decision-theoretic and game-theoretic models.
The chief innovationA shift in emphasis from truth-conditions to probabilities.
Background Pragbot
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Background Pragbot
SUBTLE
Situation Understanding Bot Through Language &Environment
SUBTLE Team“we must move from robust
sentence processing to robustutterance understanding ”
Mitch Marcus, Norm Badler,
Aravind Joshi, George Pap-pas, Fernando Pereira, MaribelRomero (Penn); Andrew andme (UMass Amherst); Holly
Yanco (UMass Lowell)
Background Pragbot
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g g
Pragbot data-gatherer
• Pragbot is a game played on the Net, in a browser.
• The players comunicate via an Instant Messaging functionthat logs all their messages and actions in the game world.
• Pragbot scenarios mirror search-and-rescue scenarios, butwith simplifications that make linguistic modelling moretractable.
(Pragbot was developed by Andrew McCallum, Chris Potts,and Karl Shultz, and coded by Karl Schultz.)
Background Pragbot
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A screenshot
Background Pragbot
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Fast and flexible data collection
Pragbot is lightweight and flexible. We have changed theinterface and the task descriptions a number of times, witheach change bringing in linguistically richer interactions.
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Illustrative data
We begin with a range of cases involving questions and theiranswers. The primary question:
What counts as a resolving answer?
We chose the data with the following general scenario in mind:
a human operator is querying a bot. The bot should giveresolving answers (where his knowledge base permits them).
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Mention-all vs. mention-some
Where can we buy supplies?
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Mention-all vs. mention-some
Where can we buy supplies?
Mention-all• Context: We’re writing a comprehensive guide to the
area.
• Resolvedness condition: An exhaustive listing of the(reasonable) shopping places.
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Mention-all vs. mention-some
Where can we buy supplies?
Mention-all• Context: We’re writing a comprehensive guide to the
area.
• Resolvedness condition: An exhaustive listing of the(reasonable) shopping places.
Mention-some• Context: We’re low on food and water.
• Resolvedness condition: Mentioning the best (closest,safest, etc.) place, or a few good options.
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Mention-all vs. mention-some
Who has a light?
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Mention-all vs. mention-some
Who has a light?
Mention-all• Context: Speaker needs to ensure that no one in the
group is going to get stopped by airport security.
• Resolvedness condition: Listing of everyone who has alight.
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Mention-all vs. mention-some
Who has a light?
Mention-all• Context: Speaker needs to ensure that no one in the
group is going to get stopped by airport security.
• Resolvedness condition: Listing of everyone who has alight.
Mention-some• Context: Speaker needs to light her cigar.
• Resolvedness condition: Just name one (friendly,willing, nearby) person with a lighter.
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Domain restrictions
What cards do you have?
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Domain restrictions
What cards do you have?
Wide domain• Context: Speaker dealt the cards and noticed that some
were missing.
• Resolvedness condition: List everything you’re holding.
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Domain restrictions
What cards do you have?
Wide domain• Context: Speaker dealt the cards and noticed that some
were missing.
• Resolvedness condition: List everything you’re holding.
Narrowed domain• Context: Speaker folds. He wants to know what beat
him.
• Resolvedness condition: Just name the good cards (if there are any).
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Domain restrictions
Example (Pragbot data)
Did you find anything?
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Domain restrictions
Example (Pragbot data)
Context: Player 2 is looking for
Player 2: Did you find anything?[...]
Player 1: yep, h at the top exit
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Domain restrictions
Example (Pragbot data)
Context: Player 2 is looking for
Player 2: Did you find anything?[...]
Player 1: yep, h at the top exit
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Domain restrictions
Example (Pragbot data)
Have you found anything?
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Domain restrictions
Example (Pragbot data)Context: The players are trying to get six consecutive hearts,but they are still in the process of deciding which six.
Player 2: i got 2H
Player 1: I found a 3HPlayer 2: sweet.
[...]
Player 1: Have you found anything?
Player 2: no, just 2H
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Domain restrictions
Example (Pragbot data)Context: The players are trying to get six consecutive hearts,but they are still in the process of deciding which six.
Player 2: i got 2H
Player 1: I found a 3HPlayer 2: sweet.
[...]
Player 1: Have you found anything?
Player 2: no, just 2H
No suggestion that Player2 didn’t see 3D, KD, etc.
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Identification conditions
Who is Arnold Schwarzenegger?
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Identification conditions
Who is Arnold Schwarzenegger?
• The governor of California.
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Identification conditions
Who is Arnold Schwarzenegger?
• A famous bodybuilder.
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Identification conditions
Who is Arnold Schwarzenegger?
• The Terminator.
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Identification conditions
Who is Arnold Schwarzenegger?
• That guy over there.
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Identification conditions
Who is Arnold Schwarzenegger?
• The governor of California.
• A famous bodybuilder.
• The Terminator.
• That guy over there.
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Levels of specificity
Who was at the meeting?
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Levels of specificity
Who was at the meeting?
General• Context: The speaker wants to get a sense for what
kind of meeting it was.• Resolvedness condition: Some linguists, some
computer scientists, some mathematicians.
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Levels of specificity
Who was at the meeting?
General• Context: The speaker wants to get a sense for what
kind of meeting it was.• Resolvedness condition: Some linguists, some
computer scientists, some mathematicians.
Specific• Context: The speaker is checking against a list of likely
attendees.
• Resolvedness condition: Chris, Alan, Mitch, . . .
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Granularity
Where are you from?
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G l
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Granularity
Where are you from?
• Massachusetts.
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G l i
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Granularity
Where are you from?
• The U.S.
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G l i
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Granularity
Where are you from?
• Planet earth.
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G l i
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Granularity
Where are you from?
• Connecticut. (My birthplace.)
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G l it
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Granularity
Where are you from?
• UMass Amherst. (My university.)
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G l it
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Granularity
Where are you from?
• Belgium. (My ancestral home.)
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Gran larit
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Granularity
Where are you from?
• Massachusetts.
• The U.S.
• Planet earth.
• Connecticut. (My birthplace.)
• UMass Amherst. (My university.)• Belgium. (My ancestral home.)
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Granularity
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Granularity
Pragbot players can’t see each other, but they must coordinatetheir movements. As a result, they ask many versions of
Where are you?
They answer at different levels of granularity depending on
• the task they were assigned
• the current subtask
• the nature of the environment• their current knowledge of each other’s whereabouts
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Granularity
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Granularity
Example (Pragbot data)Player A: Where are you?
Player B: in the first box-like region in the
center, 2nd row
Player B: I’m sort of in the middle.
Player B: still at the right bottom corner
• Unattested: “In the pragbot world”(redundant in context)
• Attested confusion: “In Northampton”(at the start of the game; players not yet fully engaged)
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Polarity variation
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Polarity variation
How high is a helicopter permitted to fly?
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Polarity variation
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Polarity variation
How high is a helicopter permitted to fly?
Lower bound• Context: We need to avoid the powerlines while still
getting close to the ground.
• Resolvedness condition: The lowest safe height.
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Polarity variation
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Polarity variation
How high is a helicopter permitted to fly?
Lower bound• Context: We need to avoid the powerlines while still
getting close to the ground.
• Resolvedness condition: The lowest safe height.
Upper bound• Context: We need to be sure the atmosphere isn’t too
thin.
• Resolvedness condition: The highest safe height.
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Gradable modifiers
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Gradable modifiers
Is the door open?
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Gradable modifiers
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Gradable modifiers
Is the door open?
Maximal interpretation
• Context: We need to get a vehicle out of the building.It barely fits through the doorway.
• Intended: Is the door completely open?
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Gradable modifiers
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Gradable modifiers
Is the door open?
Maximal interpretation
• Context: We need to get a vehicle out of the building.It barely fits through the doorway.
• Intended: Is the door completely open?
Minimal interpretation• Context: We need to secure the building.
• Intended: Is the door even a little bit open?
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Plurals
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Plurals
Are the windows are open?
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Plurals
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Plurals
Are the windows are open?
Existential reading• Context: We need to ensure the building is locked up.
• the windows ≈ some of the windows
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Plurals
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u a s
Are the windows are open?
Existential reading• Context: We need to ensure the building is locked up.
• the windows ≈ some of the windows
Universal reading• Context: We are painting the sills.
• the windows ≈ all the windows
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Pragmatically required over-answering
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g y q g
Ali calls a hotelAli: Is Lisa Simpson in Room 343?
Clerk A: She’s in room 400. (implicit “no”)
Clerk B: She checked out yesterday. (implicit “no”)
Clerk C: #No.
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Pragmatically required over-answering
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g y q g
Example (Pragbot data)
Can you take the inside of the cube.
The answers expected by the form (“yes”, “no”) areinfelicitous because their content is mutually known. (Theplayers have freedom of movement.)
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Pragmatically required over-answering
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g y q g
Example (Pragbot data)
Context: The players are planning their search strategyPlayer 1: Can you take the inside of the cube.
Player 2: ok I take the insidePlayer 1: I’ll look on the outside
The answers expected by the form (“yes”, “no”) areinfelicitous because their content is mutually known. (Theplayers have freedom of movement.)
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Pragmatically required over-answering
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g y q g
Example (Worcester Cold Storage Fire)Context: Firemen lost inside a large, maze-like building witha floor-plan that effectively changed by the minute as roomsfilled with smoke and walls collapsed.
Car 3 Okay, do we have fire coming up through
the roof yet?
L-1/P1 We have a lot of hot embers blowing
through.
Inferred pragmatically No, but . . .
(A mere “no” would be disastrous here.)
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Devious exploitation of pragmatic inferencing
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g g
From Bronston v. United States
Q: Do you have any bank accounts in Swiss banks,Mr. Bronston?
A: No, sir.Q: Have you ever?
A: The company had an account there for about six months,in Zurich.
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Devious exploitation of pragmatic inferencing
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From Bronston v. United States
Q: Do you have any bank accounts in Swiss banks,Mr. Bronston?
A: No, sir.Q: Have you ever?
A: The company had an account there for about six months,in Zurich.
The truth
Bronston once had a large personal Swiss account.
The issueThe cooperative inference of the previous slide has gotten usinto trouble here.
Partition semantics Answer values Implicatures Desiderata
Partition semantics and answer values
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Groenendijk and Stokhof (1982): the semantic value of an
interrogative is a partition of the information state W intoequivalence classes based on the extension of the questionpredicate.
Partition semantics Answer values Implicatures Desiderata
Partition semantics and answer values
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Groenendijk and Stokhof (1982): the semantic value of an
interrogative is a partition of the information state W intoequivalence classes based on the extension of the questionpredicate.
Answering
• Fully congruent answers identify a single cell.
• Partial answers overlap with more than one cell.
• Over-answers identify a proper subset of one of the cells.
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Partition semantics Answer values Implicatures Desiderata
Polar questions
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[[Did Sam laugh?]] ={v ∈ W | v ∈ [[laughed(sam)]] iff w ∈ [[laughed(sam)]]}
w ∈
[[laughed(sam)]] W − [[laughed(sam)]]
Partition semantics Answer values Implicatures Desiderata
Polar questions
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[[Did Sam laugh?]] ={v ∈ W | v ∈ [[laughed(sam)]] iff w ∈ [[laughed(sam)]]}
w ∈
[[laughed(sam)]] W − [[laughed(sam)]]
Answers
Partition semantics Answer values Implicatures Desiderata
Polar questions
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[[Did Sam laugh?]] ={v ∈ W | v ∈ [[laughed(sam)]] iff w ∈ [[laughed(sam)]]}
w ∈
[[laughed(sam)]] W − [[laughed(sam)]]
Answers
“Yes”
Partition semantics Answer values Implicatures Desiderata
Polar questions
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[[Did Sam laugh?]] ={v ∈ W | v ∈ [[laughed(sam)]] iff w ∈ [[laughed(sam)]]}
w ∈
[[laughed(sam)]] W − [[laughed(sam)]]
Answers
“No”
Partition semantics Answer values Implicatures Desiderata
Constituent questions
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[[Who laughed?]] ={v ∈ W | ∀d . [[laugh]](d )(v ) iff [[laugh]](d )(w )
w ∈ W
Partition semantics Answer values Implicatures Desiderata
Constituent questions
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[[Who laughed?]] ={v ∈ W | ∀d . [[laugh]](d )(v ) iff [[laugh]](d )(w )
w ∈ W
Answers
Partition semantics Answer values Implicatures Desiderata
Constituent questions
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[[Who laughed?]] ={v ∈ W | ∀d . [[laugh]](d )(v ) iff [[laugh]](d )(w )
w ∈ W
Answers
“Bart and Lisa”
Partition semantics Answer values Implicatures Desiderata
Constituent questions
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[[Who laughed?]] ={v ∈ W | ∀d . [[laugh]](d )(v ) iff [[laugh]](d )(w )
w ∈ W
Answers
“Bart, Lisa, Maggie, andBurns”
Partition semantics Answer values Implicatures Desiderata
Constituent questions
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[[Who laughed?]] ={v ∈ W | ∀d . [[laugh]](d )(v ) iff [[laugh]](d )(w )
w ∈ W
Answers
“No one”
Partition semantics Answer values Implicatures Desiderata
Answer valuesWe get a rough measure of the extent to which p answers Q
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We get a rough measure of the extent to which p answers Q by inspecting the cells in Q with which p has a nonemptyintersection:
Definition (Answer values)
Ans(p , Q ) = q ∈ Q | p ∩ q = ∅Example
Bart: Did Sam laugh?
Lisa:
[[laughed(sam)]] W − [[laughed(sam)]]
Partition semantics Answer values Implicatures Desiderata
Answer valuesWe get a rough measure of the extent to which p answers Q
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We get a rough measure of the extent to which p answers Q by inspecting the cells in Q with which p has a nonemptyintersection:
Definition (Answer values)
Ans(p , Q ) = q ∈ Q | p ∩ q = ∅Example
Bart: Did Sam laugh?
Lisa: Yes. | Ans | = 1
[[laughed(sam)]] W − [[laughed(sam)]]
Partition semantics Answer values Implicatures Desiderata
Answer valuesWe get a rough measure of the extent to which p answers Q
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We get a rough measure of the extent to which p answers Q by inspecting the cells in Q with which p has a nonempty
intersection:
Definition (Answer values)
Ans(p , Q ) = q ∈ Q | p ∩ q = ∅Example
Bart: Did Sam laugh?
Lisa: No. | Ans | = 1
[[laughed(sam)]] W − [[laughed(sam)]]
Partition semantics Answer values Implicatures Desiderata
Answer valuesWe get a rough measure of the extent to which p answers Q
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We get a rough measure of the extent to which p answers Q by inspecting the cells in Q with which p has a nonempty
intersection:
Definition (Answer values)
Ans(p , Q ) = q ∈ Q | p ∩ q = ∅Example
Bart: Did Sam laugh?
Lisa: I heard some giggling. | Ans | = 2
[[laughed(sam)]] W − [[laughed(sam)]]
Partition semantics Answer values Implicatures Desiderata
Over-informative answers
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Ans values are a bit too blunt, since Ans(p , Q ) = Ans(p ′, Q )wherever p ′ ⊆ p , for all questions Q .
Example
Bart: Is Sam happy at his new job?Lisa:
[[happy(sam)]] W − [[happy(sam)]]
Partition semantics Answer values Implicatures Desiderata
Over-informative answers
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Ans values are a bit too blunt, since Ans(p , Q ) = Ans(p ′, Q )wherever p ′ ⊆ p , for all questions Q .
Example
Bart: Is Sam happy at his new job?Lisa: Yes. | Ans | = 1
[[happy(sam)]] W − [[happy(sam)]]
Partition semantics Answer values Implicatures Desiderata
Over-informative answers
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Ans values are a bit too blunt, since Ans(p , Q ) = Ans(p ′, Q )wherever p ′ ⊆ p , for all questions Q .
Example
Bart: Is Sam happy at his new job?Lisa: Yes, and he hasn’t been to jail yet. | Ans | =
1
[[happy(sam)]] W − [[happy(sam)]]
Partition semantics Answer values Implicatures Desiderata
A preference ordering
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Definition (Relevance (G&S, van Rooij))p ≻Q q iff Ans(p , Q ) ⊂ Ans(q , Q ) or
Ans(p , Q ) = Ans(q , Q ) and q ⊂ p
Partition semantics Answer values Implicatures Desiderata
A preference ordering
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Definition (Relevance (G&S, van Rooij))p ≻Q q iff Ans(p , Q ) ⊂ Ans(q , Q ) or
Ans(p , Q ) = Ans(q , Q ) and q ⊂ p
ExampleIn the previous example,
[[happy(sam)]] ≻[[?happy(sam)]] [[happy(sam) ∧ no-jail(sam)]]
While their Ans values are the same, the first is a superset of the second.
Partition semantics Answer values Implicatures Desiderata
Example: Granularity
E l
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Example
Where are you from?
≈ Which planet are you from?≈ Which country are you from?≈ Which city are you from?
· · ·
Partition semantics Answer values Implicatures Desiderata
Example: Granularity
E l
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Example
Where are you from?
≈ Which planet are you from?≈ Which country are you from?≈ Which city are you from?
· · ·
Definition (Fine-grainedness (van Rooy, 2004))
A question Q is more fine-grained than question Q ′ iff
Q ⊑ Q ′ iff ∀q ∈ Q ∃q ′ ∈ Q ′ q ⊆ q ′
If Q is more fine-grained than Q ′, then an exhaustive answerto Q is more informative than an exhausitive answer to Q ′.
Partition semantics Answer values Implicatures Desiderata
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Conversational implicatures
Partition semantics Answer values Implicatures Desiderata
Partial answers
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Ans values bring us part of the way towards understanding
relevance implicatures.
Example (Partial answer)
Tom: Which city does Barbara live in?
Jerry: Barbara lives in Russia. (| Ans | > 1)• Implicature: Jerry doesn’t know which city.
Partition semantics Answer values Implicatures Desiderata
Partial answers
A l b i t f th t d d t di
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Ans values bring us part of the way towards understanding
relevance implicatures.
Example (Partial answer)
Tom: Which city does Barbara live in?
Jerry: Barbara lives in Russia. (| Ans | > 1)• Implicature: Jerry doesn’t know which city.
Example (Complete answer)
Tom: Which country does Barbara live in?Jerry: Barbara lives in Russia. (| Ans | = 1)
• No implicature about Jerry’s city-level knowledge.
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Partition semantics Answer values Implicatures Desiderata
Pragmatic principles
Let Q be the question under discussion (QUD)
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Let Q be the question under discussion (QUD).
For speakersAnswer Q with a proposition p such that
p ≻Q p ′ for all p ′ ∈ DoxS
Partition semantics Answer values Implicatures Desiderata
Pragmatic principles
Let Q be the question under discussion (QUD)
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Let Q be the question under discussion (QUD).
For speakersAnswer Q with a proposition p such that
p ≻Q p ′ for all p ′ ∈ DoxS
For hearersLet p be the speaker’s answer. For all q such that such thatq ≻Q p , the speaker is not positioned to offer q felicitously.
• If q ⊂ p , then the speaker lacks sufficient evidence for q .• If p ⊂ q , then the speaker is answering a different QUD,
thereby implicating that Q is not the right QUD.
Partition semantics Answer values Implicatures Desiderata
Desiderata
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1 Discourse participants negotiate the nature of questions.What motivates them?
Partition semantics Answer values Implicatures Desiderata
Desiderata
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1 Discourse participants negotiate the nature of questions.What motivates them?
2 It is essential that we achieve more precise statements of the implicatures and their calculations.
Partition semantics Answer values Implicatures Desiderata
Desiderata
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1 Discourse participants negotiate the nature of questions.What motivates them?
2 It is essential that we achieve more precise statements of the implicatures and their calculations.
3 Ideally, we would reduce the pragmatic principles involvedin relevance implicature calculations to something morefundamental.
Partition semantics Answer values Implicatures Desiderata
Desiderata
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1 Discourse participants negotiate the nature of questions.What motivates them?
2 It is essential that we achieve more precise statements of the implicatures and their calculations.
3 Ideally, we would reduce the pragmatic principles involvedin relevance implicature calculations to something morefundamental.
4 We’d like an account of the pragmatic variability of
questions discussed earlier (mention-some vs. mention-all,and so forth).
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Decision problems Applications Looking ahead
Decision problems
As a first step towards satisfying our desires for this analysis,
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we’ll inject some decision theory into our pragmatics, as a wayof making sense primarily of answers.
Definition (Decision problems)
A decision problem is a structure DP = (W , S , P S , A, U S ):• W is a space of possible states of affairs;
• S is an agent;
• P S is a (subjective) probability distribution (for agent S );
• A is a set of actions that S can take; and
• U S is a utility function for S , mapping action–world pairsto real numbers.
Decision problems Applications Looking ahead
Example: Schlepp the umbrella?
Example (The decision problem Schlepp)
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• W = {w 1 . . . w 10}. Assume it rains in {w 1 . . . w 7} andnot in {w 8 . . . w 10}.
• P S ({w i }) = P S ({w j }) for all w i , w j ∈ W
• A = {umbrella, no-umbrella}
• U (umbrella, w i ) = 2 if it rains in w i U (umbrella, w i ) = −2 if it doesn’t rain in w i
U (no-umbrella, w i ) = −8 if it rains in w i U (no-umbrella, w i ) = 4 if it doesn’t rain in w i
rain no rainumbrella 2 −2
no-umbrella −8 4
S is deciding under uncertainty. What’s his best move?
Decision problems Applications Looking ahead
Expected utilities
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Expected utilities take risk into account when measuring theusefulness of performing an action.
Definition
For decision problem DP = (W , S , P S , A, U S ) the expected utility of an action a ∈ A
EUDP (a) = w ∈W P ({w }) · U (a, w )
Decision problems Applications Looking ahead
Solving decision problems
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Definition (Utility value of a decision problem)Let DP = (W , S , P S , A, U S ) be a decision problem.
UV(DP ) = maxa∈A
EUDP (a)
Definition (Solving a decision problem)
Let DP = (W , S , P S , A, U S ) be a decision problem. Thesolution to DP is
choose a such that EUDP (a) = UV(DP )
Decision problems Applications Looking ahead
Solving the umbrella problem
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rain (.7) no rain (.3) EUumbrella 2 −2 .8
no-umbrella −8 4 −4.4
• UV(Schlepp) = maxa∈{umbrella,no-umbrella} EU(a)= .8
• The optimal action is umbrella.
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Decision problems Applications Looking ahead
Utility value of new informationIncoming information might change the decision problem bychanging the expected utilities.
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g g p
Definition (Conditional expected utility)
Let DP = (W , S , P S , A, U S ) be a decision problem.
EUDP (a|p ) =
w ∈W P ({w }|p ) · U (a, w )
Example• EU(no-umbrella) = −4.4
• EU(no-umbrella|{w 8, w 9, w 10}) = 4 (given no rain)
• EU(umbrella) = .8
• EU(umbrella|{w 8, w 9, w 10}) = −2 (given no rain)
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Decision problems Applications Looking ahead
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Applications
Decision problems Applications Looking ahead
Action propositions
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DefinitionIf DP = (W , S , P S , A, U S ) is a decision problem and a is anaction in A, then
a∗ = {w ∈ W | U S (a, w ) U S (a′, w ) for a′ ∈ A}
If there is a unique optimal action in every world, then A∗, theset of propositions a∗ ∈ A, is a partition. But we won’t impose
this condition.
Decision problems Applications Looking ahead
Example: Visiting Barbara
•W = {w 1, . . . , w 4}
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{ }
[[B lives in Moscow ]] = {w 1} [[B lives in Prague ]] = {w 3}
[[B lives in Petersburg ]] = {w 2} [[B lives in Budapest ]] = {w 4}
• P S ({w i }) = P S ({w j }) for all w i , w j ∈ W
• A = ax , wherex ∈ {Moscow, Petersburg, Prague, Budapest}
• U (ax , w ) = 10 if Barbara lives in x in w , elseU (ax , w ) = 0.
Decision problems Applications Looking ahead
Example: Visiting Barbara
•W = {w 1, . . . , w 4}
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[[B lives in Moscow ]] = {w 1} [[B lives in Prague ]] = {w 3}
[[B lives in Petersburg ]] = {w 2} [[B lives in Budapest ]] = {w 4}
• P S ({w i }) = P S ({w j }) for all w i , w j ∈ W
• A = ax , wherex ∈ {Moscow, Petersburg, Prague, Budapest}
• U (ax , w ) = 10 if Barbara lives in x in w , elseU (ax , w ) = 0.
Action propositions
a∗Moscow = {w 1} a∗Prague = {w 3}
a∗Petersburg = {w 2} a∗Budapest = {w 4}
Decision problems Applications Looking ahead
Resolving the problem
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ExampleAssume the decision problem that Bart’s question gives rise to(or, the one that gives rise to his question) is as before.
Bart: Where does Barbara live? {w 1} {w 2}
{w 3} {w 4}
Lisa: Russia.⇒ Does not resolve the decision problem.
Lisa: Petersburg (Moscow, Prague, . . . ).
⇒ Resolves the decision problem
Decision problems Applications Looking ahead
Example: Which country?
•W = {w 1, . . . , w 4}
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{ 1, , 4}
[[B lives in Moscow ]] = {w 1} [[B lives in Prague ]] = {w 3}
[[B lives in Petersburg ]] = {w 2} [[B lives in Budapest ]] = {w 4}
• P S ({w i }) = P S ({w j }) for all w i , w j ∈ W
• A = ax , where x ∈ {Russia, Czech, Budapest}• U (ax , w ) = 10 if Barbara lives in x in w , else
U (ax , w ) = 0.
Decision problems Applications Looking ahead
Example: Which country?
•W = {w 1, . . . , w 4}
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{ , , }
[[B lives in Moscow ]] = {w 1} [[B lives in Prague ]] = {w 3}
[[B lives in Petersburg ]] = {w 2} [[B lives in Budapest ]] = {w 4}
• P S ({w i }) = P S ({w j }) for all w i , w j ∈ W
• A = ax , where x ∈ {Russia, Czech, Budapest}• U (ax , w ) = 10 if Barbara lives in x in w , else
U (ax , w ) = 0.
Action propositions a∗Russia = {w 1, w 2}
a∗Czech = {w 3} a∗Hungary = {w 4}
Decision problems Applications Looking ahead
Resolving the problem
Bart: Where does Barbara live? {w 1} {w 2}{w 3} {w 4}
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Lisa: Russia.
⇒ Resolves the decision problem even though it doesn’tcorrespond to a cell in Bart’s question.
Decision problems Applications Looking ahead
Resolving the problem
Bart: Where does Barbara live? {w 1} {w 2}{w 3} {w 4}
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Lisa: Russia.
⇒ Resolves the decision problem even though it doesn’tcorrespond to a cell in Bart’s question.
Lisa: Petersburg (Moscow, Prague, . . . ).
⇒ Resolves the decision problem but provides too muchinformation.
Decision problems Applications Looking ahead
Resolving the problem
Bart: Where does Barbara live? {w 1} {w 2}{w 3} {w 4}
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Lisa: Russia.
⇒ Resolves the decision problem even though it doesn’tcorrespond to a cell in Bart’s question.
Lisa: Petersburg (Moscow, Prague, . . . ).
⇒ Resolves the decision problem but provides too muchinformation.
p ≻Q q iff Ans(p , Q ) ⊂ Ans(q , Q ) or
Ans(p , Q ) = Ans(q , Q ) and q ⊂ p
p ≻A∗ q iff Ans(p , A∗) ⊂ Ans(q , A∗) or
Ans(p , A∗) = Ans(q , A∗) and q ⊂ p
Decision problems Applications Looking ahead
Mention-some questions
Example (Craige Roberts)
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I’m working on a rush plumbing project and need some parts.Where can one buy faucet washers?
Decision problems Applications Looking ahead
Mention-some questions
Example (Craige Roberts)
I’m working on a rush plumbing project and need some parts.
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g p g p j p
Where can one buy faucet washers?
•
W = {w 1
, . . . , w 3}
[[Parts at Moe’s ]] = {w 1, w 2} [[Parts at Larry’s ]] = {w 2, w 3}• P S ({w i }) = P S ({w j }) for all w i , w j ∈ W •
U w 1 w 2 w 3aMoe’s 10 10 0
aLarry’s 0 10 10
Decision problems Applications Looking ahead
Mention-some questions
Example (Craige Roberts)
I’m working on a rush plumbing project and need some parts.
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g p g p j p
Where can one buy faucet washers?
•
W = {w 1
, . . . , w 3}
[[Parts at Moe’s ]] = {w 1, w 2} [[Parts at Larry’s ]] = {w 2, w 3}• P S ({w i }) = P S ({w j }) for all w i , w j ∈ W •
U w 1 w 2 w 3aMoe’s 10 10 0
aLarry’s 0 10 10
a∗Moe’s = {w 1, w 2} a∗Larry’s = {w 2, w 3}
Decision problems Applications Looking ahead
Domain restrictions
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Example (van Rooy 2003)
I fold. I’m curious about whether I did the right thing.
What (cards) do you have?
Decision problems Applications Looking ahead
Domain restrictions
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Example (van Rooy 2003)
I fold. I’m curious about whether I did the right thing.
What (cards) do you have?
A choice of domain leads to a choice of granularity for A∗.
The order ≻A∗ can then home in on the optimal choice.
Decision problems Applications Looking ahead
Expected utility values of questionsEUVDP (Q ) gives the average utility of the members of Q .
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DefinitionLet DP = (W , S , P S , A, U S ) be a decision problem. Then
EUVDP (Q ) =
q ∈Q P S (q ) · UV DP (q )
The following ordering is determined largely by EUV, but itresorts to the measure of granularity to resolve ties.
Definition
Q ≻DP Q ′ iff EUVDP (Q ) > EUVDP (Q
′) orEUVDP (Q ) = EUVDP (Q
′) and Q ′ ⊏ Q
Decision problems Applications Looking ahead
Pragmatic principles, decision-theoretically
Let DP I ,J = (W , S , P I ,J , A, U I ,J ) be a pair of decisionproblems differing only in the agent (I or J ).
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Decision problems Applications Looking ahead
Pragmatic principles, decision-theoretically
Let DP I ,J = (W , S , P I ,J , A, U I ,J ) be a pair of decisionproblems differing only in the agent (I or J ).
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For interrogator I Ask a question Q such that
Q ≻DP I
Q ′ for all Q ′ ∈ ℘(℘(W ))
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Decision problems Applications Looking ahead
Pragmatic principles, decision-theoretically
Let DP I ,J = (W , S , P I ,J , A, U I ,J ) be a pair of decisionproblems differing only in the agent (I or J ).
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For interrogator I Ask a question Q such that
Q ≻DP I
Q ′ for all Q ′ ∈ ℘(℘(W ))
For the witness J Answer Q with a proposition p such that
p ≻A∗ p ′ for p ′ ∈ DoxJ
In both cases, the speaker’s behavior is shaped by the decisionproblem.
Decision problems Applications Looking ahead
Looking ahead
1 C ti th j t b b M l d (2006 b) f
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1 Continue the project begun by Malamud (2006a,b) of extending van Rooy’s (2004) approach to questions intonew areas:
Decision problems Applications Looking ahead
Looking ahead
1 C ti th j t b b M l d (2006 b) f
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1 Continue the project begun by Malamud (2006a,b) of extending van Rooy’s (2004) approach to questions intonew areas:
• Situations (what counts as minimal?)
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Decision problems Applications Looking ahead
Looking ahead
1 Continue the project begun by Malamud (2006a b) of
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1 Continue the project begun by Malamud (2006a,b) of extending van Rooy’s (2004) approach to questions intonew areas:
• Situations (what counts as minimal?)• Reference (which mode is best?)• Comparatives (which contextual standard?)
Decision problems Applications Looking ahead
Looking ahead
1 Continue the project begun by Malamud (2006a b) of
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1 Continue the project begun by Malamud (2006a,b) of extending van Rooy’s (2004) approach to questions intonew areas:
• Situations (what counts as minimal?)• Reference (which mode is best?)• Comparatives (which contextual standard?)
2 Further articulate the role of decisions by moving to agame-theoretic setting.
Decision problems Applications Looking ahead
Looking ahead
1 Continue the project begun by Malamud (2006a b) of
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1 Continue the project begun by Malamud (2006a,b) of extending van Rooy’s (2004) approach to questions intonew areas:
• Situations (what counts as minimal?)• Reference (which mode is best?)• Comparatives (which contextual standard?)
2 Further articulate the role of decisions by moving to agame-theoretic setting.
3 Get a better grip on how these pragmatic factors can
influence embedded readings.
References
References I
Aloni, Maria. 2000. Quantification under Conceptual Covers . Ph.D. thesis, Universiteitvan Amsterdam, Amsterdam. Published in the ILLC Dissertation Series, 2001-1.
Bach, Kent. 1999. The semantics–pragmatics distinction: What it is and why itmatters In Ken Turner ed The Semantics Pragmatics Interface from Different
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Bach, Kent. 1999. The semantics pragmatics distinction: What it is and why itmatters. In Ken Turner, ed., The Semantics–Pragmatics Interface from Different Points of View , 65–84. Oxford: Elsevier. URLhttp://online.sfsu.edu/~kbach/spd.htm.
Beaver, David Ian. 2001. Presupposition and Assertion in Dynamic Semantics .Stanford, MA: CSLI.
Beck, Sigrid and Hotze Rullmann. 1999. A flexible approach to exhaustivity in
questions. Natural Language Semantics 7(3):249–298.ten Cate, Balder and Chung-Shieh Shan. 2007. Axiomatizing Groenendijk’s Logic of
Interrogation. In Maria Aloni; Alastair Butler; and Paul Dekker, eds., Questions inDynamic Semantics , volume 17 of Current Research in the Semantics/Pragmatics Interface , 63–82. Amsterdam: Elsevier.
Devitt, Michael and Kim Sterelny. 1987. Language and Reality: An Introduction to the Philosophy of Language . Cambridge, MA: MIT Press.
Ginzburg, Jonathan. 1996. Interrogatives: Questions, facts, and dialogue. In ShalomLappin, ed., The Handbook of Contemporary Semantic Theory , 385–422. Oxford:Blackwell.
Ginzburg, Jonathan and Ivan A. Sag. 2001. Interrogative Investigations: The Form,Meaning, and Use of English Interrogatives . Stanford, CA: CSLI.
References
References IIGroenendijk, Jeroen. 1999. The logic of interrogation. In Tanya Matthews and Devon
Strolovitch, eds., Proceedings of SALT IX , 109–126. Ithaca, NY: Cornell University.Groenendijk, Jeroen and Martin Stokhof. 1982. Semantic analysis of wh-complements.
Linguistics and Philosophy 5(2):175–233.K d Ch i t h 2007 V d Th ti f l ti d
http://online.sfsu.edu/~kbach/spd.htmhttp://online.sfsu.edu/~kbach/spd.htmhttp://online.sfsu.edu/~kbach/spd.htmhttp://online.sfsu.edu/~kbach/spd.htmhttp://online.sfsu.edu/~kbach/spd.htm
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g p y ( )Kennedy, Christopher. 2007. Vagueness and grammar: The semantics of relative and
absolute gradable adjective. Linguistics and Philosophy 30(1):1–45.Kennedy, Christopher and Louise McNally. 2005. Scale structure and the semantic
typology of gradable predicates. Language 81(2):345–381.Levinson, Stephen C. 2000. Presumptive Meanings: The Theory of Generalized
Conversational Implicature . Cambridge, MA: MIT Press.
Malamud, Sophia. 2006a. (Non)-maximality and distributivity: A decision theoryapproach. Paper presented at SALT 16, Tokyo, Japan.
Malamud, Sophia. 2006b. Semantics and Pragmatics of Arbitrariness . Ph.D. thesis,Penn.
Roberts, Craige. 1996. Information structure: Towards an integrated formal theory of pragmatics. In Jae Hak Yoon and Andreas Kathol, eds., OSU Working Papers inLinguistics , volume 49: Papers in Semantics, 91–136. Columbus, OH: The OhioState University Department of Linguistics. Revised 1998.
van Rooy, Robert. 2003. Questioning to resolve decision problems. Linguistics and Philosophy 26(6):727–763.
van Rooy, Robert. 2004. Signalling games select Horn strategies. Linguistics and Philosophy 27(4):493–527.
References
References III
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Rullmann, Hotze. 1995. Maximality in the Semantics of WH-Constructions . Ph.D.thesis, UMass Amherst. Published by the GLSA.
Schulz, Katrin and Robert van Rooij. 2006. Pragmatic meaning and non-monotonicreasoning: The case of exhaustive interpretation. Linguistics and Philosophy 29(2):205–250.
Solan, Lawrence M. and Peter M. Tiersma. 2005. Speaking of Crime: The Language of Criminal Justice . Chicago, IL: University of Chicago Press.Vermeulen, Kees. 2000. Information in discourse: A game for many agents. In
Lawrence Cavdeon; Patrick Blackburn; Nick Braisby; and Atsushi Shimojima, eds.,Logic, Language and Computation, volume 3, chapter 15, 295 – 318. CSLIPublications.