By Josh, Kayla, Lauren
The puzzle we are addressing is: How do listeners make sense of metaphorical or figurative utterances, such as “John is a whale,” when those utterances are not literally true?
For example, when someone says “John is a whale,” we intuitively understand they are likely commenting on John’s size, not that he’s actually a marine mammal. This model simulates how pragmatic reasoning allows listeners to arrive at that kind of inference by modeling the beliefs, goals, and choices of both the speaker and the listener.
In the very first part of the code, we define the categoriesPrior. John can either be a whale or a person, but there’s only a 1% probability that he’s actually a whale. This reflects our common-sense belief that people are typically people.
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is extremely unlikely that John is actually a whale.
var categoriesPrior = function() {
categorical([0.01, 0.99], categories)
}
The utterancePrior function treats both “whale” and “person” as equally likely choices. This means the model assumes they are equally easy to say. Therefore, there’s no cost difference driving the choice.
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
Now we move to featureSets, which lay out eight possible combinations of features John might have. These features are: large, graceful, and majestic. Each one of these features is represented in binary numbers.
The featureSetPrior function then assigns probabilities to each combination based on whether John is a person or a whale. This reflects empirical world knowledge. For example, the first feature set has the highest probability when John is a whale. That is because whales are more often all three of those things than people are.
So this function shows how the model uses real-world associations between category and traits to help inform interpretation.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
Now we model what the speaker might be trying to communicate, which is the role of the goalPrior. Here, we assume the speaker could be trying to highlight any one of the three traits: large, graceful, or majestic. Additionally, each of these traits has equal probability. So the model starts out with no bias about which trait the speaker is focused on.
We then define a goalState function, which checks if a given set of features satisfies a goal. For instance, if the speaker wants to communicate that John is majestic, and John is in fact majestic, then goalState returns 1—this goal is met.
To keep things consistent, the model uses literalInterpretation to make sure the utterance aligns with the literal category. So if the speaker says “whale,” it assumes John must be a whale.
One important parameter here is alpha, set to 3. This controls how strongly the speaker prefers informative utterances. A higher alpha means the speaker is more pragmatic, making it more likely to choose an utterance that effectively communicates the intended trait.
While the speaker selects an utterance to highlight a single trait, the listener does not know which trait that is. Instead, the listener infers the likelihood of all traits jointly, given the utterance.
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Prior probability of speaker's goal is set to uniform but can
// change with context/QUD.
var goalPrior = function() {
categorical([1,1,1], goals)
}
// Speaker optimality parameter
var alpha = 3
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
In the case of the literal listener, it hears an utterance like “whale,” starts by considering both categories equally, and samples a feature set based on the category.
Then, it begins to filter responses: it only keeps interpretations where the category matches the utterance. Hence, “whale” means John must be a whale.
Finally, it checks whether the sampled features satisfy the communicative goal using goalState.
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
The speaker, on the other hand, knows both John’s actual features and the specific trait they want to communicate.
The speaker then evaluates both possible utterances—“person” and “whale”—by simulating how well each one would help the literal listener infer the intended trait.
This is where factor comes in. It redistributes the speaker’s choices: the better an utterance leads the listener to the correct inference, the more likely the speaker is to use it. This is the model’s way of favoring informative, goal-relevant speech.
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful
: graceful, majestic : majestic})))
return utterance
}})
}
The pragmatic listener, implemented as pragmaticListener(utterance), models how listeners infer intended meaning behind figurative language. It starts by sampling a possible category for John using categoriesPrior() and then draws a set of traits from featureSetPrior(category).
It also samples a communicative goal using goalPrior(), representing which trait the speaker might be trying to highlight, such as largeness, gracefulness, or majesty.
The crucial step is the observe function, which filters for cases where a speaker with those traits and that goal would have actually chosen the utterance that was heard. The Infer function uses this filtering to generate updated beliefs about John’s likely category and traits.
Although the statement “John is a whale” is literally false, the model shows how a listener can infer that John likely has a whale-like quality, such as being very large. This reflects how people use pragmatic reasoning to go beyond literal meaning.
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
Both the hyperbole and metaphor models involve the use of a speaker, pragmatic listener, factor, and alpha. The speaker in both models chooses what to say that would get the listener to get to the point. The pragmatic listener hears the utterances and infers what is being said, along with the reasoning behind it. In terms of factor and observe, the speaker utilizes factor to score each utterance, with more informative ones being scored higher. Observe is used by the listener as it runs the speaker model, depending on which utterance was actually said.
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
QUD (question under discussion) and goal both communicate the importance in the model and attempt to address it by shaping what the speaker chooses to say.
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Prior probability of speaker's goal is set to uniform but can
// change with context/QUD.
var goalPrior = function() {
categorical([1,1,1], goals)
}
The differences between the two models are the utterances and how they work with the model, the process of understanding. For the hyperbole model, it utilizes approximation of values since precise values are more costly. On the other hand, the metaphor model uses binary entities to mark which trait is more likely tied to the utterance, John or whale. As the literal listener only accepts literal matches, the literal meaning is not probable due to prior probabilities. The pragmatic listener then utilizes the speaker model and the prior probabilities to infer that the utterances are not to be taken literally, but intertwined in intention. Simply put, the pragmatic listener processes the intended meaning rather than what is actually being stated.
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is extremely unlikely that John is actually a whale.
var categoriesPrior = function() {
categorical([0.01, 0.99], categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
Below is the result produced when putting in “viz.hist(pragmaticListener(“whale”))” to visualize the probability of what utterance is more likely to be referred to when the pragmatic listener hears whale.
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is extremely unlikely that John is actually a whale.
var categoriesPrior = function() {
categorical([0.01, 0.99], categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Prior probability of speaker's goal is set to uniform but can
// change with context/QUD.
var goalPrior = function() {
categorical([1,1,1], goals)
}
// Speaker optimality parameter
var alpha = 3
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
viz.hist(pragmaticListener("whale"))
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is extremely unlikely that John is actually a whale.
var categoriesPrior = function() {
categorical([0.01, 0.99], categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Prior probability of speaker's goal is set to uniform but can
// change with context/QUD.
var goalPrior = function() {
categorical([1,1,1], goals)
}
// Speaker optimality parameter
var alpha = 3
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
viz.table(pragmaticListener("whale"))
viz.marginals(pragmaticListener("whale"))
Above is the default prediction of the metaphor model (viz.table(pragmaticListener(“whale”))) and visualizations of its marginal distributions (viz.marginals(pragmaticListener(“whale”))). All displays show what the pragmatic listener believes upon hearing the utterance “John is a whale,” specifically what they believe about the species of the subject as well as which features the subject has (large, graceful and/or majestic).
As is apparent in both the table and marginal distribution, the person category completely dominates the whale category in terms of probability. This division of categories is a result of the extreme imbalance in the categoriesPrior, which assigns a weight of 0.99 to person and 0.01 to whale via a categorical draw. In reality, a speaker is much more likely to be talking about a person than a whale at any given point, which is reflected in this categoriesPrior.
Looking at the table, we also see patterns among the feature distributions within each category. It is always most likely that the pragmatic listener believes the subject will have all three features, then ⅔ features, then ⅓ features, then none of the features. The more features a person or whale has, the more informative the utterance “John is a whale” becomes, and it is assumed that the speaker is always trying to be as informative as possible. This assumption is also supported by the marginal distributions of the features. For all features, the pragmatic listener believes that it is more likely the feature is true of the subject than not true. It would not make sense for “not true” to be the more likely belief, because that would make the utterance more uninformative.
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is equally likely that John is a whale or a person.
var categoriesPrior = function() {
uniformDraw(categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Prior probability of speaker's goal is set to uniform but can
// change with context/QUD.
var goalPrior = function() {
categorical([1,1,1], goals)
}
// Speaker optimality parameter
var alpha = 3
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
viz.table(pragmaticListener("whale"))
viz.marginals(pragmaticListener("whale"))
Above is the prediction that the model produces when the categoriesPrior is changed from a categorical([0.01, 0.99], categories) draw to uniformDraw (still running viz.table(pragmaticListener(“whale”)) and viz.marginals(pragmaticListener(“whale”))). It is no longer the case that person completely dominates whale; now, the pragmatic listener believes that whale is actually more likely to be the subject of the utterance than person, as seen in the marginal distribution. The interpretation of the utterance “John is a whale” is notably more literal, which may be the case in situations where one is as likely to encounter a whale as a person (say, while whale-watching). We also observe a slight increase in the probability of all features being true of the subject in their respective marginal distributions.
Because the categoriesPrior is now neutralized, the results of this version can be explained by other parameters of the model. In the original model, the optimality parameter alpha = 3, which is considerably higher than the default alpha value of 1 from other models we looked at in class. Neutralizing the alpha parameter by setting it to 1, or making it more extreme by setting it to 10, yields different predictions for the pragmatic listener (see below). With respect to alpha = 3, reducing the value of alpha distributes probability more evenly across the items in the table and increasing alpha pulls probability towards the already high-probability items.
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is equally likely that John is a whale or a person.
var categoriesPrior = function() {
uniformDraw(categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Prior probability of speaker's goal is set to uniform but can
// change with context/QUD.
var goalPrior = function() {
categorical([1,1,1], goals)
}
// Speaker optimality parameter (un-comment each string to see predictions)
// var alpha = 1
// var alpha = 10
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
viz.table(pragmaticListener("whale"))
viz.marginals(pragmaticListener("whale"))
Another parameter which influences the probability order of items is the featureSetPrior, which has assigned probabilities to category and feature combinations according to data from Kao et al. (2014).
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is extremely unlikely that John is actually a whale.
var categoriesPrior = function() {
categorical([0.01, 0.99], categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Probability of speaker's goal being "large" is double that of other goals.
var goalPrior = function() {
categorical([2,1,1], goals)
}
// Speaker optimality parameter
var alpha = 3
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
viz.table(pragmaticListener("whale"))
viz.marginals(pragmaticListener("whale"))
Above is the prediction produced by the model when the probability of the speaker’s goal being to communicate that the subject is large is doubled in the goalPrior (still running viz.table(pragmaticListener(“whale”)) and viz.marginals(pragmaticListener(“whale”))). Previously, all three of the features were equally as likely to be the speaker’s goal, but this change might more accurately reflect the intentions of a real-world speaker saying, “John is a whale,” based on common uses of the metaphor. While the categoriesPrior has been reset to its default categorical draw, within each category, all items that include the large feature are more likely than those which exclude it. In the marginal distribution, we also see that the probability of the pragmatic listener believing the subject is large is double that of their belief that the subject is not large. The goals of the pragmatic speaker affect the pragmatic listener’s predictions because the speaker exists within the pragmatic listener, and the speaker is assumed to be truthful. If the pragmatic listener knows that the speaker’s primary goal is to communicate that the subject is large, and that the speaker is truthful, it follows that the pragmatic listener believes the subject is indeed large.
However, when privileging the other goals, we do not observe the same feature dominance of graceful and majestic as we do for large in the pragmatic listener predictions (see below). This disparity can be attributed to the featureSetPrior, which itself privileges the four combinations which include the large feature over the sets of four which include the graceful and majestic features, especially in the whale category.
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is extremely unlikely that John is actually a whale.
var categoriesPrior = function() {
categorical([0.01, 0.99], categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// One goal has double the probability of the other two (un-comment each string to see predictions)
// var goalPrior = function() {
// categorical([1,2,1], goals)
// }
// var goalPrior = function() {
// categorical([1,1,2], goals)
// }
// Speaker optimality parameter
var alpha = 3
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
viz.table(pragmaticListener("whale"))
viz.marginals(pragmaticListener("whale"))
Thus far, all of the alternate predictions I have explored are those that show what the pragmatic listener thinks upon hearing the utterance, “John is a whale.” The remainder of this write-up will analyze what the model predicts when the pragmatic listener hears the utterance, “John is a person” (viz.table(pragmaticListener(“person”))).
// John could either be a whale or a person.
var categories = ["whale", "person"]
// It is extremely unlikely that John is actually a whale.
var categoriesPrior = function() {
categorical([0.01, 0.99], categories)
}
// The speaker could either say "John is a whale" or "John is a person."
var utterances = ["whale", "person"]
// The utterances are equally costly.
var utterancePrior = function() {
categorical([1,1], utterances)
}
// The features of John being considered are "large", "graceful",
// "majestic." Features are binary.
var featureSets = [
{large : 1, graceful : 1, majestic : 1},
{large : 1, graceful : 1, majestic : 0},
{large : 1, graceful : 0, majestic : 1},
{large : 1, graceful : 0, majestic : 0},
{large : 0, graceful : 1, majestic : 1},
{large : 0, graceful : 1, majestic : 0},
{large : 0, graceful : 0, majestic : 1},
{large : 0, graceful : 0, majestic : 0}
]
// information about feature priors (probabilistic world knowledge)
// obtained by an experimental study (see paper)
var featureSetPrior = function(category) {
category === "whale" ? categorical([0.30592786494628, 0.138078454222818,
0.179114768847673, 0.13098781834847,
0.0947267162507846, 0.0531420411185539,
0.0601520520596695, 0.0378702842057509],
featureSets) :
category === "person" ? categorical([0.11687632453038, 0.105787535267869,
0.11568145784997, 0.130847056136141,
0.15288225956497, 0.128098151176801,
0.114694702836614, 0.135132512637255],
featureSets) :
true
}
// Speaker's possible goals are to communicate feature 1, 2, or 3
var goals = ["large", "graceful", "majestic"]
// Prior probability of speaker's goal is set to uniform but can
// change with context/QUD.
var goalPrior = function() {
categorical([1,1,1], goals)
}
// Speaker optimality parameter
var alpha = 3
// Check if interpreted category is identical to utterance
var literalInterpretation = function(utterance, category) {
utterance === category
}
// Check if goal is satisfied
var goalState = function(goal, featureSet) {
goal === "large" ? featureSet.large :
goal === "graceful" ? featureSet.graceful :
goal === "majestic" ? featureSet.majestic :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function() {
var category = uniformDraw(categories)
var featureSet = featureSetPrior(category)
condition(literalInterpretation(utterance, category))
return goalState(goal, featureSet)
}})
}
// Speaker model
var speaker = function(large, graceful, majestic, goal) {
Infer({model: function() {
var utterance = utterancePrior()
factor(alpha *
literalListener(utterance,goal).score(goalState(goal, {large : large, graceful : graceful, majestic : majestic})))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function() {
var category = categoriesPrior()
var featureSet = featureSetPrior(category)
var large = featureSet.large
var graceful = featureSet.graceful
var majestic = featureSet.majestic
var goal = goalPrior()
observe(speaker(large, graceful, majestic, goal), utterance)
return {category, large, graceful, majestic}
}})
}
viz.table(pragmaticListener("person"))
viz.marginals(pragmaticListener("person"))
Inputting this utterance negates the function of the metaphor model entirely. While the whale utterance can be used in this case to refer to either a person or a whale, the person utterance can only ever describe a person. Upon hearing the utterance, “John is a person,” there is only a miniscule chance that the pragmatic listener thinks John is a whale.
If it is true that John is a person, then it is most likely that John has none of the features of a whale, and least likely that John has all of the features of a whale. This pattern can be observed in both the table and the marginal distribution graphs. Using the utterance “John is a person” when John is a person communicates nothing about John’s features, but the pragmatic listener gleans some information from the fact that the speaker did not choose to say “John is a whale.” Because the whale utterance is also an option, the pragmatic listener infers that the speaker would have used that utterance if John had any features of a whale.
On the very off chance that John is a whale (a category which receives probability only because whales exist), the relative likelihood of feature set combinations is determined mainly by the featureSetPrior.