By Lai
It is an irony model in which the utterance’s meaning is intended to describe the opposite of the real meaning. For instance, today is a beautiful day but I tell you the weather is “terrible”, you will not think that I am trying to convey the information literally. You realize that I am trying to convey the information ironically, so I am actually telling you the weather is really good. The following model has three conversational goals: communicating about the true state, communicating about the speaker’s valence (i.e., whether they feel positively or negatively toward the state), and communicating about the speaker’s arousal (i.e., how strongly they feel about the state).
The RSA model used here is to model the situation that people say ironic utterances, and there are three kinds of participants here. LiteralListener represents people who make reflections on what they hear, and they don’t have the prior knowledge, like today is a beautiful day. Speakers have the prior knowledge and they know how the LiteralListener responds, and they respond with an utterance, which can let the LiteralListener know the state with the highest probability. Finally, we have PragmaticListener who also has the prior knowledge, and they hear the utterance that the speaker responds with. Then they analyze what state, valence, and arousal the speaker wants to convey.
// There are three possible states the weather could be in:
// terrible, ok, or amazing
var states = ['terrible', 'ok', 'amazing']
// Since we are in California, the prior over these states
// are the following. Once could also imagine this being
// the prior in a certain context, e.g. when it's clearly
// sunny and nice out.
var statePrior = function() {
categorical([1, 50, 50], states)
}
Infer(statePrior)
First we get the state and statePrior. The three states to describe the weather are “terrible”, “ok”, and “amazing”. The statePrior is categorical, which is actually because both the listener and speaker have the prior that today is a beautiful day. Therefore we have more prior probability for the ok and amazing.
// Valence prior defined in terms of negative valence.
// If the current state is terrible, it's extremely likely
// that the valence associated is negative. If it's ok, then
// the valence could be negative or positive with equal
// probability.
var valencePrior = function(state) {
state === "terrible" ? flip(0.99) ? -1 : 1 :
state === "ok" ? flip(0.5) ? -1 : 1 :
state === "amazing" ? flip(0.01) ? -1 : 1 :
true
}
Infer(valencePrior)
valencePrior represents the negative valence that people feel. If their current state is “terrible”, it is extremely likely that their valence is negative, which is equal to -1. If their current state is “ok”, it is equally likely that their valence is negative or positive, so both sides have 50% probability. If their current state is “amazing”, it is extremely likely that their valence is positive, which is equal to 1. Then the code will be, if the state is “terrible”, then flip the coin. There is a 99% probability to be True. If it is True, get -1. If it is false, get 1. If the state is “ok”, then flip the coin. There is a 50% probability to be True. If the state is amazing, then flip the coin. There is only a 1% probability to be True.
// Define binary arousals (could model as continuous).
var arousals = ["low", "high"]
var arousalPrior = function(state) {
state === "terrible" ? categorical([0.1, 0.9], arousals) :
state === "ok" ? categorical([0.9, 0.1], arousals) :
state === "amazing" ? categorical([0.1, 0.9], arousals) :
true
}
Infer(arousalPrior)
There are arousals “low” and “high” to describe how people feel about the state. If the state is “terrible” or “amazing”, it is a categorical draw that there are much more probabilities to have a strong feeling, so the probability is 0.9 for “high” and 0.1 for “low”. If the state is “ok”, it reverses: the probability is 0.1 for “high” and 0.9 for “low”.
// Define goals and goal priors. Could want to communicate state of the world,
// valence about it, or arousal (intensity of feeling) about it.
var goals = ["goalState", "goalValence", "goalArousal"]
var goalPrior = function() {
categorical([1, 1, 1], goals)
}
// Assume possible utterances are identical to possible states
var utterances = states
// Assume cost of utterances is uniform.
var utterancePrior = function() {
uniformDraw(utterances)
}
goals is the QUD that a speaker is likely addressing with their utterance. There are three QUDs here, State, Valence, and Arousal. Each has equal prior probability. There are three utterances, the same as the states, “terrible”, “ok”, and “amazing”, but the prior will be the uniformDraw, same probability for the three utterances.
// Literal interpretation is just whether utterance equals state
var literalInterpretation = function(utterance, state) {
utterance === state
}
// A speaker's goal is satisfied if the listener infers the correct
// and relevant information.
var goalState = function(goal, state, valence, arousal) {
goal === "goalState" ? state :
goal === "goalValence" ? valence :
goal === "goalArousal" ? arousal :
true
}
The literalInterpretation is to let the utterance equal the state, so the speaker will choose the utterances in the three states “terrible”, “ok”, and “amazing”. goalState is the QUD that asks the speaker to answer, and how the goal matches the goalState.
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function(){
var state = uniformDraw(states)
var valence = valencePrior(state)
var arousal = arousalPrior(state)
condition(literalInterpretation(utterance,state))
return goalState(goal, state, valence, arousal)
}})
}
For the literalListener, this is the function with arguments utterance and goal. They hear an utterance and a goal. state is from uniformDraw, valence is from valencePrior, and arousal is taken from arousalPrior. The condition of literalInterpretation lets the utterance equal the state. Then literalListener returns the goalState which matches the goal they hear.
// Define a speaker
var speaker = function(state, valence, arousal, goal) {
Infer({model: function(){
var utterance = utterancePrior()
factor(1 * literalListener(utterance,
goal).score(goalState(goal,
state,
valence,
arousal)))
return utterance
}})
}
For the speaker, this is the function with arguments state, valence, arousal, and goal. They learn the actual state, valence, and arousal, and they hear the QUD they will answer. The utterance is taken from utterancePrior.
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function(){
var state = statePrior()
var valence = valencePrior(state)
var arousal = arousalPrior(state)
var goal = goalPrior()
observe(speaker(state, valence, arousal, goal),utterance)
return {state, valence, arousal}
}})
}
The pragmaticListener is the function with argument utterance. The pragmaticListener only hears the utterance, and they take state from statePrior, valence from valencePrior, arousal from arousalPrior, and goal from goalPrior. They observe how the speaker sees the state, valence, arousal, goal, and how the speaker uses the utterance to answer. Finally they return the types of state, valence, arousal with probability.
Similarity: This model is similar to the hyperbole model in that both models are under the situation that you have the probabilities for each state and valence beforehand. And they both include the QUDs to answer. So this is the situation for both models to predict how they will interpret the non-literal utterances. For example, in the hyperbole model, people have price prior $50 with high probability, but they hear $50000. In the irony model, people have state prior “amazing” or “ok” with high probability, but they hear “terrible”.
Difference: The difference is that the irony model adds one QUD, arousal, in the model. The arousal is used to test how strongly they feel about the state. The reason to add the arousal is to make certain for the PragmaticListener that they consider the state is “amazing”. If there is no arousal QUD, the return with most probability when the PragmaticListener hears “terrible” will be “ok”.
The following is the whole code.
// There are three possible states the weather could be in:
// terrible, ok, or amazing
var states = ['terrible', 'ok', 'amazing']
// Since we are in California, the prior over these states
// are the following. Once could also imagine this being
// the prior in a certain context, e.g. when it's clearly
// sunny and nice out.
var statePrior = function() {
categorical([1, 50, 50], states)
}
// Valence prior defined in terms of negative valence.
// If the current state is terrible, it's extremely likely
// that the valence associated is negative. If it's ok, then
// the valence could be negative or positive with equal
// probability.
var valencePrior = function(state) {
state === "terrible" ? flip(0.99) ? -1 : 1 :
state === "ok" ? flip(0.5) ? -1 : 1 :
state === "amazing" ? flip(0.01) ? -1 : 1 :
true
}
// Define binary arousals (could model as continuous).
var arousals = ["low", "high"]
// Define goals and goal priors. Could want to communicate state of the world,
// valence about it, or arousal (intensity of feeling) about it.
var goals = ["goalState", "goalValence", "goalArousal"]
var goalPrior = function() {
categorical([1, 1, 1], goals)
}
// Assume possible utterances are identical to possible states
var utterances = states
// Assume cost of utterances is uniform.
var utterancePrior = function() {
uniformDraw(utterances)
}
// Sample arousal given a state.
var arousalPrior = function(state) {
state === "terrible" ? categorical([0.1, 0.9], arousals) :
state === "ok" ? categorical([0.9, 0.1], arousals) :
state === "amazing" ? categorical([0.1, 0.9], arousals) :
true
}
// Literal interpretation is just whether utterance equals state
var literalInterpretation = function(utterance, state) {
utterance === state
}
// A speaker's goal is satisfied if the listener infers the correct
// and relevant information.
var goalState = function(goal, state, valence, arousal) {
goal === "goalState" ? state :
goal === "goalValence" ? valence :
goal === "goalArousal" ? arousal :
true
}
// Define a literal listener
var literalListener = function(utterance, goal) {
Infer({model: function(){
var state = uniformDraw(states)
var valence = valencePrior(state)
var arousal = arousalPrior(state)
condition(literalInterpretation(utterance,state))
return goalState(goal, state, valence, arousal)
}})
}
// Define a speaker
var speaker = function(state, valence, arousal, goal) {
Infer({model: function(){
var utterance = utterancePrior()
factor(1 * literalListener(utterance,
goal).score(goalState(goal,
state,
valence,
arousal)))
return utterance
}})
}
// Define a pragmatic listener
var pragmaticListener = function(utterance) {
Infer({model: function(){
var state = statePrior()
var valence = valencePrior(state)
var arousal = arousalPrior(state)
var goal = goalPrior()
observe(speaker(state, valence, arousal, goal),utterance)
return {state, valence, arousal, goal}
}})
}
viz.table(literalListener("terrible", "goalState"))
viz.table(speaker("terrible", -1, "high", "goalValence"))
viz.table(pragmaticListener("terrible"))
We can see that when the LiteralListener hears “terrible”, they think that the state will be “terrible”. When the PragmaticListener hears “terrible”, the two states with most probability are “amazing”, 1, and “high”, and “ok”, -1, “low”. The reason the state is “amazing” and “ok” is that the PragmaticListener has the prior statePrior with really high probability for “amazing” and “ok”. When they think the state is “amazing”, they think the valence is 1, and arousal is “high”. When they think the state is “ok”, valence is -1, and arousal is “low”. The reason the valence is -1 but not 1 for state “ok” is that they still hear the utterance “terrible” from the speaker. Therefore, they may think that the true valence is -1 but not 1.
In addition, when we change or add the goal in the return of pragmaticListener, we can see that for the highest probability condition with state “amazing”, the PragmaticListener thinks that the speaker answers the goalArousal question, and this is because they think the arousal QUD is the most informative. “Amazing” and “terrible” have the same arousalPrior.