Running Head: EMOTION IN THEORY OF MIND

Computational models of emotion inference in Theory of Mind:
A review and roadmap

Desmond C. Onga,b, Jamil Zakic, and Noah D. Goodmanc,da

A*STAR Artificial Intelligence Initiative, Agency for Science, Technology and Research(A*STAR), SingaporebInstitute of High Performance Computing, Agency for Science, Technology and Research(A*STAR), SingaporecdDepartment of Psychology, Stanford University

Department of Computer Science, Stanford University
In Press at: Topics in Cognitive Science

Special Issue on: Computational Approaches to Social Cognition
Final version dated: 1 July 2017 (Minor edits to funding acknowledgements)

Address Correspondence to:
Desmond C. Ong
A*STAR Artificial Intelligence Initiative
Agency for Science, Technology and Research, Singapore 138632
desmond.c.ong@gmail.com
Author Contributions: D.C.O., J. Z., and N. D. G. wrote the paper.
The authors declare no conflict of interest.
Keywords: Emotion; Affective Cognition; Inference; Theory of Mind

EMOTION IN THEORY OF MIND

2
ABSTRACT

Research on social cognition has fruitfully applied computational modeling approaches to
explain how observers understand and reason about others’ mental states. By contrast, there has
been less work on modeling observers’ understanding of emotional states. We propose an
intuitive theory framework to studying affective cognition---how humans reason about emotions--and derive a taxonomy of inferences within affective cognition. Using this taxonomy, we
review formal computational modeling work on such inferences, including: causal reasoning
about how others react to events, reasoning about unseen causes of emotions, reasoning withmultiple cues, as well as reasoning from emotions to other mental states. Additionally, we
provide a roadmap for future research by charting out inferences---such as hypothetical andcounterfactual reasoning about emotions---that are ripe for future computational modeling work.
This framework proposes unifying these various types of reasoning as Bayesian inference within
a common “intuitive Theory of Emotion”. Finally, we end with a discussion of important
theoretical and methodological challenges that lie ahead in modeling affective cognition.

EMOTION IN THEORY OF MIND

3

Recent developments in computational cognitive modeling have allowed
researchers to specify and test precise hypotheses about how people make inferences
about their social world. These include inferences about what others desire and believe
about the world (e.g., Baker, Jara-Ettinger, Saxe, & Tenenbaum, 2017; Goodman et al,2006), what others mean when they use language to communicate (Goodman & Frank,
2016; Goodman & Stuhlmüller, 2013; Frank & Goodman, 2012), and what future decisions
others might make (Jara-Ettinger, Gweon, Schulz, & Tenenbaum, 2016; Jern & Kemp, 2015).
These recent developments comprise the focus of the current special issue. However, thesemodels have often neglected how people reason about one of the most essential elementsof human psychology: emotions.
Emotions play a central role in our social lives. They signal people’s immediate
reactions to events in the world (e.g., Ellsworth & Scherer, 2003), and cause many
behaviors---both intentional and unintentional (Lerner, Li, Valdesolo, & Kassam, 2015;
Loewenstein & Lerner, 2003). Given the importance of emotions in social interactions, it ishardly surprising that people are naturally attuned to perceiving and understanding
emotions in those around them (Harris, 1989; Zaki & Ochsner, 2011).
In this paper, we consider the present and future of computational modeling inunderstanding how people reason about emotional states---what we term affective
cognition (Ong, Zaki, & Goodman, 2015). We adopt an intuitive theory framework to thestudy of affective cognition, using which we derive a taxonomy of affective cognitive
inferences (in the spirit of Adelson & Bergen, 1991, and Kemp & Jern, 2013, who
respectively derived taxonomies of visual functions and inductive problems). Thistaxonomy encompasses a wide range of lay reasoning about emotional states, such as usingEMOTION IN THEORY OF MIND

4

observed behavior or situation contexts (or combinations thereof) to infer emotions andother mental states (e.g., De Melo, Carnevale, Read, & Gratch, 2014; Wu, Baker, Tenenbaum,& Schulz, 2018; Zaki, 2013). Finally, we provide a roadmap for future research, byhighlighting inferences that have yet to be studied computationally, and by discussing
important theoretical and methodological challenges that lie ahead.

Laying out an intuitive theory of emotions
People have rich intuitive theories of how others around them think and behave,allowing them to infer others’ motivations and explain others’ behavior (e.g., Heider, 1958;
Gopnik & Meltzoff, 1997; Ross, 1977). An intuitive theory of other people consists of first, a
structured ontology of concepts---for example, personality, goals, behavior---and second,the causal relationships relating these concepts (Gerstenberg & Tenenbaum, 2017). These
intuitive theories allow laypeople to make sense of others around them, in a similar fashion
to how scientific theories allow scientists to explain the physical world (Carey, 2009;
Wellman & Gelman, 1992).
People also possess a rich intuitive theory of emotions that comprises conceptual
knowledge about different emotional states (e.g., anger, happiness) and how they are
related to their causes and effects. People (“observers”) use their intuitive theory of
emotion to reason about the emotional states of others (“agents”) around them, andthereby decide how best to respond in social situations. Importantly, these intuitive
theories comprise the observer’s beliefs about how others’ emotions work, which dependon the observer’s past history and their subjective beliefs. Though the observer’s beliefs
may not necessarily reflect the reality of how emotions “actually work”, these beliefs

EMOTION IN THEORY OF MIND

5nevertheless form the basis for how the observer understands and interacts with thosearound them (e.g., Gopnik & Meltzoff, 1997; Ross, 1977).
An intuitive theory of emotion contains two important types of causal relationships.
The first connects emotions to their causes: what, in the observer’s mind, causes an agent
to feel an emotion? The second involves the effects of emotion: what, in the observer’s
mind, does an agent’s emotion cause them to do? These components and their relationships
are represented in Figure 1.

Figure 1: A model of an intuitive theory of emotion, unifying ideas from de Melo et al(2014), Ong, Zaki, & Goodman (2015), Saxe and Houlihan (2017), and Wu et al (2018). We
use standard graphical model notation: shaded circles represent observable variables,
while unshaded circles represent latent variables. We render variables at the subsequent“time-step” translucent. Arrows represent a directed causal relationship, and bolded lettersdenote the abbreviations used in equations. The observer applies a “third-person
appraisal” process to reason about how (i) the outcome of an event that an agent
experiences, and (ii) the agent’s mental states (beliefs and desires), together result in theagent experiencing emotions. The agent’s emotions in turn cause the agent to display
emotional expressions, and take intentional actions that lead to new outcomes andupdated mental states (and new emotions).
Intuitive causes of emotions
People intuitively expect that others’ emotions arise as a reaction to motivationallysalient events. In addition to the outcome of these events, people also use their knowledge
about others’ mental states—such as others’ beliefs and desires—to reason about how
others feel. This intuitive understanding of how event outcomes and mental states impact
emotions emerges early in life (Gross & Ballif, 1991; Harris, 1989; Lagattuta, Wellman, &EMOTION IN THEORY OF MIND

6

Flavell, 1997; Repacholi, Meltzoff, Hennings, & Ruba, 2016; Wu, Muentener, & Schulz,2017): toddlers and infants understand that an agent’s display of happiness reflects asatisfied desire, while an agent’s display of sadness reflects a thwarted goal (Repacholi &Gopnik, 1997; Skerry & Spelke, 2014; Wellman, Phillips, & Rodriguez, 2000). By preschool,
children associate a surprised emotional expression with a mismatch between reality andthe agent’s prior beliefs about the world (Wellman & Banerjee, 1991; Wu & Schulz, 2017),
and factor agents’ expectations into attributions of the agent’s emotions (Ong, Asaba, &Gweon, 2016). Adults similarly draw rich inferences from an agent’s emotional reactions totheir latent beliefs and desires (Scherer & Grandjean, 2008; Wu et al, 2018; Van Kleef, De
Dreu, & Manstead, 2010). Thus, the intuitive theory of emotion relates an agent’s mental
states (specifically, their beliefs about the world, and their desires), and the outcome ofan event that the agent experiences, to the agent’s emotions (Fig. 1).
How do people understand the way event outcomes and the agent’s mental statesgive rise to emotions? One idea is that people may engage a similar reasoning process to
how they themselves experience events firsthand. According to appraisal theories of
emotion (Arnold, 1960; Ellsworth & Scherer, 2003; Moors, Ellsworth, Scherer & Frijda,
2013; Ortony, Clore, & Collins, 1988; Smith & Lazarus, 1993), an agent’s emotions arise
from an evaluation (“appraisal”) of outcomes along various self-relevant dimensions, suchas whether the outcomes contribute to or detract from the agent’s goals (“goalconduciveness”). If Sally judges her job offer as facilitating her career goals, she would
likely feel happy.
Many researchers have proposed that laypeople perform a similar appraisal-likeprocess to reason about others’ emotions (De Melo et al, 2014; Ong, Zaki, & Goodman,

EMOTION IN THEORY OF MIND

7

2015; Seimer & Reisenzein, 2007; Skerry & Saxe, 2015; Wondra & Ellsworth, 2015; Wu etal, 2018; Van Kleef et al, 2010)---we term this process “third-person appraisal”. That is,when an observer considers an agent experiencing an outcome, the observer first reduces
the outcome to a small number of features that the observer thinks is relevant to the agent,and then uses that evaluation to judge the agent’s emotions. For example, observers
intuitively evaluate, from the agent’s perspective, an outcome’s goal-conduciveness andwhether the outcome was expected. If Bob learns that Sally just received glowing
performance reviews, and knows of her goals of getting promoted, he would reason thatshe probably feels a positively-valenced emotion. If Bob additionally knows that Sally did
not expect the performance reviews, he might predict that she would also feel surprised.
Appraisal is especially important from a computational standpoint. The situations thatagents experience in daily life vary widely along an innumerable number of dimensions,and (the observer’s theory of) an agent’s appraisal reduces the complexities of everyday
situations to a small set of relevant “features” that are important for the agent’s well-being.
It is also important to note that the observer’s appraisal on behalf of the agent may differ
from the agent’s own appraisal in two key ways. First, the observer’s set of emotionallyrelevant features, encapsulated within their intuitive theory, may not be the same as the setof features that the agent themselves consider, such as when an observer brings theirculturally held norms about emotions to assess an outcome experienced by an agent from adifferent culture. Second, the observer’s third-person appraisals depend on the observer’s
inferences of the agent’s prior beliefs and desires, which may be different from the agent’strue mental states. If Bob thought that Sally had known about her performance reviews
beforehand, he would not have predicted her surprise.

EMOTION IN THEORY OF MIND

8

These first few pieces of a model of the intuitive theory (see left half of Fig. 1),
describe the observer’s rich causal knowledge about how outcomes and the agent’s mental
states “cause” emotion. This reasoning from outcomes and mental states to emotions relies
on a contextualized, third-person appraisal process, which we will describe in greater
detail later. We turn next to the right half of Figure 1.

Intuitive effects of emotions
People also intuitively reason about what behaviors emotions cause. For one,emotional agents produce a wide variety of emotional expressions. Decades of scientificresearch have shown that people can reliably recognize emotions from facial expressions(Ekman, Friesen, & Ellsworth, 1972; Elfenbein, & Ambady, 2002; Russell, Bachorowski, &Fernández-Dols, 2003), body language (Dael, Mortillaro, & Scherer, 2012), as well as
emotional vocalizations and other paralinguistic changes in speech (Banse, & Scherer,
1996; Johnstone & Scherer, 2000; Scherer, 2003). Along with emotional displays, emotions
also influence the intentional actions that the agent may take next (Lerner et al, 2015;
Loewenstein & Lerner, 2003). Fear may produce a tendency to flee, anger may prompt
someone to approach and confront a threat, and happiness might engender prosocial
behavior (e.g., Frijda, Kuipers, & Ter Schure, 1989; Isen, 1987). People are intuitively
sensitive to how emotions can influence others’ actions; for example, people use a partner’s
emotional displays to infer how cooperative they would be (Krumhuber et al, 2007; Levine,
Barasch, Rand, Berman, & Small, 2018; Van Cleef et al, 2010). In the intuitive theory in
Figure 1, we have placed emotional expressions and intentional actions as downstream
effects of emotion, reflecting the intuitive notion that emotions “cause” these two types of

EMOTION IN THEORY OF MIND

9behavior. Both types of behavior are readily observable in daily life and provide crucial
signals that allow observers to reason “backwards” to infer the agent’s latent emotion.

A Taxonomy of Affective Cognitive Inferences within the Intuitive Theory
In the previous Section, we laid out a model of an intuitive theory of emotion (Figure1) by considering how emotions are related to their two antecedent causes and their two
consequent effects. Using this intuitive theory, we can derive a taxonomy of inferences via
exhaustive enumeration (see Supplementary Material). Treating the model in Figure 1 as a
Bayesian network, we first wrote out all the 47 possible inferences that have emotion as
one of the variables---for example, P(emotion|outcome), inferring emotions from outcomes,or P(expression|emotion), reasoning about expressions from emotions. Next, we removed
26 inferences that reduced to simpler inferences based on conditional independence1.
Third, we classified the remaining 21 inferences into six categories. Finally, we added aseventh category to account for counterfactual inferences, such as inferring emotions if agiven outcome had not occurred, P(emotion|not outcome). This is summarized in Table 1.

1 For example, under the model, P(outcome|emotion, expression) reduces toP(outcome|emotion) as outcomes and expressions are independent given emotions (dseparation, e.g., Koller & Friedman, 2009).

EMOTION IN THEORY OF MIND
Categories
EmotionRecognition

10

Description
Infer an agent’s emotions fromemotional expressions (facial
expressions, body language,
prosody),or from their actions.

Inferences
P(e|x)
P(e|a)

Third-person
appraisals

Reason “forward” about how an
event would cause an agent to feel,given also their mental states.

P(e|o)
P(e|o,b,d)P(e|b,d)Given lose-wallet,
Infer P(sad)Inferringcauses ofemotions

Reason “backwards” about theevents that caused an agent’s
emotions.

P(o|e)
P(o|e,b,d)Given sad,
Infer P(losewallet)

Emotional Cue
Integration

Given multiple, potentiallyconflicting cues (e.g., multiple
behaviors and/or causes of
emotion), combine them andreason about agent’s emotions

e.g., P(e|o,x) Given smile + loseP(e|o,a)wallet,P(e|a,x)Infer P(happy),
P(e|o,b,d,a,x) P(sad), etc.

ReverseAppraisal

Given an event and an agent’s
emotions, reason backwards tomental states like beliefs anddesiresP(b,d|e,o)P(b,d|e)Given: receive-gift +surprise + happy,
Infer GiftUnexpected + GiftDesired

Predictions(Hypothetical
Reasoning)

Given an agent’s emotions, predict
subsequent behavior.
Or, given a (hypothetical) situation,
predict the agent’s emotions.

P(a|e)
P(x|e)

If anger,predict P(scoldothers)

e.g.,
P(e|not o)P(a|not e)

Given: “lose-walletand sad”,
reason that:“if not-lose-wallet,
then not-sad”

Counterfactual Given a state of the world and an
Reasoning (and agent’s emotions, reason about
Explanations)emotions or behavior incounterfactual states of the world.
This also allows explanations ofemotions or behavior in terms of
their causes.

ExamplesGiven smile,
Infer P(happy)
Given scold-others,
Infer P(anger)or, reason that: “sadbecause lose-wallet”

Table 1: A taxonomy of inferences within Affective Cognition, derived from the model in
Figure 1. P(X) denotes the probability of X occurring. The lists of inferences presented foreach category are exhaustive (given our derivation), except for the Cue Integration andCounterfactual Reasoning categories.

EMOTION IN THEORY OF MIND

11

1. Emotion Recognition
Perhaps the easiest category of lay inference is inferring someone’s emotional statefrom their emotional expressions, often called emotion recognition (e.g., Elfenbein &Ambady, 2002). The deceptive ease by which laypeople “read” emotional expressions has
led many researchers to assume perfect emotion recognition in their models, withoutmodeling this process as an inference in its own right (e.g., de Melo et al, 2014; Wu et al,2018).
In reality, laypeople’s emotion recognition is not perfectly accurate, nor is ithomogenous across all observers. First, such inferences are heavily dependent on context:
Both intense positive and negative events may sometimes produce perceptually-similar
facial expressions, making it difficult for lay observers to accurately infer emotions solely
from expressions (Aviezer, Trope, & Todorov, 2012; Carroll & Russell, 1996; Wenzler et al,2016). Second, people from different cultures differ systematically in how they perceive
emotions from facial expressions (Gendron, Roberson, van der Vyver, & Barrett, 2014; Jack,
Blais, Scheepers, Schyns, & Caldara, 2009; Russell, 1994; Yuki, Maddux, & Masuda, 2007).
Such inferences rely on lay observers’ intuitive theories, which in turn depend on theircultural background and past history (Jack, Caldara, & Schyns, 2012). Indeed, these culturaldifferences have been found to impact even how observers attend to and use low-levelfacial cues when judging emotions: for example, East Asian participants tend to fixate
longer on the eye region than Western participants (Jack et al, 2009; Yuki et al, 2007).
More recently, researchers have started building formal computational models of
how observers infer emotions from low-level features of facial expressions (Delis et al,
2016; Jack et al, 2012; Martinez & Du, 2012) and body language (Schindler, Van Gool, & de

EMOTION IN THEORY OF MIND

12

Gelder, 2008). Using conditional probability notation, modeling emotion recognition
corresponds to estimating the probability of a latent emotion e given an emotional
expression x, or P(e|x). The general recipe followed by these studies first requires some
representation of the emotional expression---for example, a popular representation for
facial expressions is the Facial Action Coding System (Ekman & Friesen, 1978). Next, one
measures how human observers classify stimuli into pre-defined emotion categories, i.e.,empirically measuring P(e|x) for say, the six “basic” emotion categories. Finally, one thenmodels the emotion recognition process P(e|x) by training classifiers using sophisticatedmachine learning techniques. Such work is relatively new, and there is still much more to
be done in modeling human emotion recognition from expressions and also from otherbehavior: this will provide a crucial foundation for many of the more complex inferences
we discuss below.

2. Third-person appraisal
Computational approaches allow researchers to quantitatively model how people
reason about an agent’s response to an experienced event. This involves, as mentioned, athird-person appraisal process that reduces the outcome that an agent experiences into asmall set of features that the observer thinks is important to the agent’s emotions (e.g.,
Skerry & Saxe, 2015). To study this appraisal process in a controlled scenario, we designed
a gambling scenario where we could parametrically vary the payoff amounts andprobabilities, and we measured how people’s judgments of an agent’s emotions after thegamble depended upon these gamble features (Ong, Zaki, & Goodman, 2015). We foundthat participants’ emotion judgments depended not only on the amount won, but how

EMOTION IN THEORY OF MIND

13much the agent won compared to the expected value of the gamble, often called aprediction error (e.g., Sutton & Barto, 1998), suggesting that participants evaluated theagent’s earnings relative to a reference point, rather than judging their earnings in absoluteterms. We also found that lay participants judged agents to react more strongly to negative
prediction errors than to positive prediction errors. These third-person findings are
strikingly consistent with influential scientific theories of first-person utility, especiallynotions of reference-dependent utility and loss aversion (Kahneman & Tversky, 1979;
Kermer, Driver-Linn, Wilson, & Gilbert, 2006; Mellers Schwartz, Ho, & Ritov, 1997). Finally,
participants believed that agents would feel worse if they came very “close” to winning thenext higher outcome, compared to if agents were not close to winning the better outcome(Ong, Goodman, & Zaki, 2015). That is, participants’ intuitive theories were also sensitive tothe “closeness” of alternative outcomes (Gleicher et al, 1990; Kahneman & Tversky, 1982;
Johnson, 1986), which have yet to feature in first-person appraisal theories.
The situation features we studied---prediction errors and the “closeness” of theoutcome to alternative outcomes---are well-defined within our experimental scenario, butmuch more work is needed to study third-person appraisals in more complex, real-world
situations. The main challenges for future research would be defining a comprehensive
representation for the many appraisal dimensions---using lists from first-person appraisal
theory (e.g., Ellsworth & Scherer, 2003; Ortony et al, 1988), or via “data-driven” approaches
like representational similarity analyses (Skerry & Saxe, 2015)---and modeling how people
map these appraisal dimensions onto emotions. There also exists many technicalchallenges in automatically extracting these appraisal dimensions from naturalistic sources

EMOTION IN THEORY OF MIND

14

like visual scenes or vignette descriptions, themselves problems at the forefront of modern
computer science.

3. Inferring causes of emotions
Given an observed emotion, people can also reason “backwards” about potential
causes of that emotion. Upon encountering a sad friend, most people would start
generating potential causes of the friend’s sadness, such as their possibly failing an exam.
Intuitively, these possibilities vary in how likely they were to have happened: failing an
exam is more likely when one is a student, but less likely after one has graduated. They also
range in how likely they were to have caused the observed emotion: a hysterically bawling
friend probably experienced something worse than a failed exam. People intuitively agree
that a potential cause with a high probability of occurring and a high probability of causing
the observed emotion is a more likely candidate than either one with a lower probability ofoccurring or one with a lower causal strength.
One way to mathematically describe this reasoning is via Bayesian inference. First,
we represent the third-person appraisal process as P(e|o), a collection of probability
distributions of emotion e given an outcome o2. Then, by Bayes’ Rule, we can write theposterior probability P(o|e), the probability of outcome o given emotion e, as:

P (o|e) / P (e|o)P (o).

(Eqn. 1)The posterior probability (e.g., P(fail-exam|sad)) is proportional to both the likelihood ofthat outcome causing the emotion (e.g., how likely is it that failing an exam will cause one’s

2 For the moment, we leave out the agent’s beliefs and desires in the appraisal process. We

add them later in the section on “reverse appraisal”.

EMOTION IN THEORY OF MIND

15

friend to be sad, P(sad|fail-exam)) and the prior probability of that outcome occurring (e.g.,
how likely is it that they had just failed an exam, P(fail-exam)). We tested whether Equation
1 provides a good model of participants’ inferences of the posterior in an experiment withthe same gambling context described in the previous section. Participants observed theemotions that the agent ostensibly felt after playing a gamble, as well as the possible
outcomes, and were tasked with inferring how likely it was that each of the outcomesoccurring. We found that a model based on Bayes’ rule (Eqn. 1) accurately predicted
participants’ judgments of the posterior probabilities of unseen gamble outcomes (Ong,Zaki, & Goodman, 2015), lending support to the claim that laypeople’s affective cognition
relies on a coherent use of a rich intuitive theory. Indeed, recent evidence suggests thateven infants are sensitive to these causal probabilities, actively searching for hidden causes
when faced with an emotion that is improbable given the observed cause (Wu et al, 2017).
Inferring causes of emotions relies on first understanding the third-person appraisal
process, and so the challenges inherent in modeling the third-person appraisal process also
apply here. In addition, Equation 1 requires the observer to consider a set of possible
outcomes. One challenge for future researchers is to define the set of possible outcomesthat laypeople intuitively shortlist and consider, as well as the prior probabilities thatlaypeople assign those outcomes. Estimating such knowledge is also a key problem faced
when applying Bayesian models to other forms of cognition (e.g., causal induction; Griffiths,
2017).

EMOTION IN THEORY OF MIND

16

4. Emotional Cue Integration
People have little difficulty reasoning about the emotions that result fromexperiencing situation outcomes (P(e|o)), or identifying the emotions that produce
observed facial expressions (P(e|x)). In real life, however, people are often presented withcombinations of multiple cues to an agent’s emotions, and have to reconcile these multiple
cues, an issue of emotional cue integration (Ong, Zaki, & Goodman, 2015; Skerry & Saxe,
2014; Zaki, 2013). Perhaps Alice knows that a friend has lost his job (a negative outcome),
but sees a smile on his face (a positive expression). How does she make sense of this?
Scientists have long pondered the relative importance of situation contexts andemotional expressions to observers’ judgments of emotions, especially in cases wherethese cues conflict (e.g., Goodenough & Tinker, 1931). On the one hand, scholars haveargued that facial expressions evolved to communicate, and hence are (always) veridical
cues to an agent’s emotion (e.g., Buck, 1994). Thus, since the jobless friend is smiling, theymust be happy, because smiling evolved to communicate happiness, and they would not besmiling otherwise. On the other hand, a wealth of other studies show that laypeople
sometimes weight the situational context and other behavioral cues over facial expressions
when attributing emotions (Aviezer et al., 2008, Caroll & Russell, 1996; Kayyal, Widen, &Russell, 2015; see Ong, Zaki, & Goodman, 2015, for a more detailed discussion). This
impasse underscores the need for a precise theory of how different cues are weighted andintegrated.
Within our framework, emotional cue integration is simply a “higher-order”
inference that relies on the simpler inferences discussed earlier. Given the causal model in
Figure 1, we can write out a precise and optimal formula for how an observer should

EMOTION IN THEORY OF MIND

17

integrate these different sources of information: For example, the probability of a latentemotion e given an observed outcome o and expression x, P(e|o,x), is given by:

P (e|o, x) /P (e|o)P (e|x)
P (e).

(Eqn. 2)

Note that this inference integrates both the probability of the emotion given the outcome,P(e|o), and the probability of the emotion given the facial expression, P(e|x), inferences we
discussed earlier. Unlike prior work in resolving cue conflict, this model does not assume apriori that any one type of cue (e.g., facial expressions) is more “privileged”, but weighs thecues according to their reliability in predicting the agent’s latent emotion. To verify thismodel, we ran a series of experiments where we presented participants with combinationsof outcomes (the outcome of a gamble that the agent experienced) and agents’ emotional
expressions (either a facial expression or verbal utterance). A Bayesian model based on
Equation 2 accurately predicted lay observers’ judgments of agents’ emotions given these
multiple cues (Ong, Zaki, & Goodman, 2015). This model predicts that observers will besensitive to the reliabilities of cues in context, and allows for observers to weigh outcomes,
faces, body expressions, and other cues to differing amounts depending on the context.
Emotional cue integration is not limited to simple two-cue combinations. Under thisBayesian framework, cue integration is any higher-order inference that relies in part on
single-cue inferences like third-person appraisal (P(e|o,b,d)) and emotion recognition(P(e|x), P(e|a)): Once one has models of these simpler inferences, one can derive inference
from any combination of cues.

EMOTION IN THEORY OF MIND

18

5. Reverse Appraisal: Inferring mental states from emotions
People not only draw inferences about an agent’s emotions, but also use emotions
to reason backwards about an agent’s appraisals and mental states (e.g., Hareli &Hess, 2010; Scherer & Grandjean, 2008). In particular, emotional reactions provide
information as to whether an agent’s goals were met and whether they expected a given
outcome. A positive/negative emotional expression may signal that the outcome wascongruent/incongruent with an agent’s desires, and a surprised expression might signalthat the outcome was unexpected given their beliefs. Comparing to the third-person
appraisal process that maps outcomes and mental states to emotions, this current piece of
reasoning works in reverse, taking an outcome and observed expression to infer the agent’s
mental states---what de Melo and colleagues (2014) term “reverse appraisal”.
Extending the formalism in previous sections, given a model of the appraisal processfrom the outcome and the agent’s beliefs and desires P(e|o,b,d), we can write an inference
similar to Equation 1 for the agent’s beliefs and desires:

P (b, d|e, o) / P (e|b, d, o)P (b, d).
This, however, requires an inference of the latent emotion. If, instead, what we actuallyobserve is an emotional expression x and the outcome o, and we are only interested in themental states, we can marginalize out the latent emotion:

P (b, d|x, o) / P (b, d)Xe

P (x|e)P (e|b, d, o)(Eqn. 3)Note that in the previous sections (e.g., Eqns. 1-2), the appraisal process was encapsulatedin P(e|o); here, we explicitly represent the agent’s beliefs and desires, so now we write theappraisal process as P(e|b,d,o). As discussed earlier, this process itself factors throughEMOTION IN THEORY OF MIND

19

quantities such as the prediction error of the outcome. In Equation 3, the goal of theinference is the conditional probability of the agent’s beliefs and desires; the agent’s
emotions are only an “intermediate” quantity that we can marginalize (or sum out). Fromright to left, the expression in Equation 3 considers the product of (i) the probability of anemotion e being a result of a belief, desire, and outcome P(e|b,d,o) (i.e., the appraisal
process) and (ii) the probability of the emotion e resulting in the observed expression
P(x|e). We then consider all possible emotions e by summing this product over all possible
emotions (“marginalizing” out e). Finally, this term is multiplied with the prior probabilityof that combination of belief and desire, P(b,d).
To test if laypeople’s inferences can be modeled by such a Bayesian model, Wu andcolleagues (2018; Experiment 3) constructed scenarios where agents performed an action(putting a white powder into a colleague’s coffee), witnessed the resultant outcome (theagent’s colleague living or dying), and displayed an emotional reaction (e.g., a surprised
facial expression). Participants read about these sequences of events, and provided
judgments of the agent’s beliefs (what the agent thought the powder was: poison or sugar)
and desires (whether or not the agent wanted to harm her colleague). Wu and colleagues(2018) present a graphical model and an inference equation similar to Figure 1 andEquation 3. We note two key differences: first, their posterior has an additional conditional
dependence on the agent’s actions (i.e., P(b,d|x,o,a))---we chose not to add actions into
Equation 3 for simplicity. Second, they assumed perfect emotion recognition and hence did
not explicitly model the latent emotion as an intermediate quantity between the outcome
and the agent’s expression. Their Bayesian model accurately tracked participants’EMOTION IN THEORY OF MIND

20

inferences of the agent’s beliefs and desires, providing further evidence that people reason
about others’ emotional and mental states using a coherent intuitive theory.
In addition, inferring others’ appraisals is also important in predicting their future
behavior. For example, if someone chooses to cooperate with you on a task, and smiles
after doing so, you may infer that they had intended to cooperate, liked the outcome, andwill likely do so again. By contrast, if they frowned instead of smiled, your inferences andyour subsequent behavior in response would be very different: perhaps they regretted
cooperating, and might not cooperate next time (see also Levine et al, 2018). De Melo andcolleagues (2014) modeled these inferences of appraisals from emotional expressions in astylized social dilemma game where two players each chose between a mutually beneficial
option and a selfish option that benefitted oneself at the expense of one’s partner. Someparticipants played against a partner who smiled after mutual cooperation, while otherparticipants saw their partner frown after mutual cooperation. De Melo and colleagues(2014) proposed and found support for a “reverse appraisal” model whereby participants
inferred either a cooperative or competitive intent from their partner’s emotional
expressions, and these inferences mediated participants’ subsequent behavior in futureinteractions.
Mental and emotional states are intimately related, and here we discussed modelinginferences of mental states from emotional information. Such work is crucial to integrateemotions into existing models of Theory of Mind (e.g., Baker, Saxe, & Tenenbaum, 2009;
Baker et al, 2017). There exist many open questions that arise from such integration ofemotions and mental states: For example, there are many complex interactions between
desires and emotions: on the one hand, people have goals to regulate emotions, but

EMOTION IN THEORY OF MIND

21conversely, emotions themselves influence how people prioritize their existing goals. How
do laypeople reason about these, and how can researchers fit them both into a causal
model? These are important psychological questions that should be addressed in future
models of social and affective cognition.

6. Predictions (Hypothetical Reasoning)
Lay reasoning about others’ emotions is not limited to the here and now; People canreason about others’ potential behavior given a future or hypothetical emotion (P(x|e),P(a|e)). Reasoning hypothetically involves using one’s intuitive theory to reason aboutnovel scenarios that could be in the possible future, or merely in the realm of imagination.
Planning a romantic marriage proposal involves incessant simulation of possible worlds
and emotions in those worlds. Indeed, experiments that prompt participants for emotion
attributions to a fictional character in a vignette or cartoon all invoke hypotheticalreasoning, and the ease with which people engage in hypothetical reasoning is crucial totheir enjoyment of film and fiction.
Hypothetical reasoning can be modeled by simply allowing the inferred variables tobe hypothetical, for example, estimating the behavior given a hypothetical emotion P(a|e).
Within Bayesian modeling, this can be operationalized as sampling “posterior predictives”
under the model (i.e., conditional predictions of new data), and has been applied to model
lay predictions in other domains (Griffiths & Tenenbaum, 2006), but not yet in affective
cognition. Future work should focus on applying such techniques to model laypeople’s
predictions of (hypothetical) emotions. Such work has important implications for designing

EMOTION IN THEORY OF MIND

22

computational agents that have to simulate and forecast their human user’s emotions andbehavior.

7. Counterfactuals Reasoning (and Explanations)
The final category of inferences in our taxonomy is counterfactual reasoning
about emotions. While the previous few sections have touched upon reasoning about
emotions given a state of the world, people can also reason about others’ emotions in statesof the world that are different from the existing reality (Gleicher et al, 1990; Johnson,1986). Indeed, emotions like regret are characterized by counterfactual reasoning (Beck &Crilly, 2009). Counterfactual thinking, like hypothetical reasoning, relies on a rich causal
model that the observer can mentally manipulate to reason about other possible worlds(Byrne, 2002; Roese, 1997). Would Carol not be sad if she had not lost her wallet (P(sad |not lose-wallet))? Would Charlie have been less curt if he had not just lost his job?
Reasoning with counterfactuals also allows observers to provide explanations(Lagnado, Gerstenberg, & Zultan, 2013; Halpern & Pearl, 2005) for others’ emotions andbehavior (Malle, 1999, 2011). Explanation within affective cognition involves assigningcausality of an emotion or a behavior to their possible causes (Böhm & Pfister, 2015; Ong,
Zaki, & Goodman, 2016). Was Tim’s disappointment after his speech due to his stutteringor the difficult questions he received after (or perhaps, both)? Explanations are importantin choosing interventions to regulate the agent’s emotions. If one thinks that Tim felt that
his talk had not gone well because of the difficult questions he received, one might try
helping Tim reappraise the difficult questions as a signal of engagement, not disdain, fromthe audience. Forming explanations and identifying the causes of behavior is also

EMOTION IN THEORY OF MIND

23

important in assigning responsibility, as in moral or legal judgments (e.g., Alicke, Mandel,
Hilton, Gerstenberg, & Lagnado, 2015), especially in legal systems with lay juries.
Although there has not yet been any work in computationally modelingcounterfactual reasoning in affective cognition, the use of probabilistic causal models torepresent the intuitive theory of emotions should allow an immediate application ofexisting techniques (e.g., Pearl, 2001, 2009). Similar probabilistic models have recently
been used in modeling lay counterfactual reasoning in other domains (Lucas & Kemp,
2015; Oaksford & Chater, 2010). We anticipate that future research will soon apply formal
techniques to model counterfactual reasoning in affective cognition.

Discussion
In this paper we have outlined a framework for understanding affective cognition
as inference within an intuitive theory of emotion. We derived a taxonomy of inferences(Table 1), and we have discussed these inferences both with respect to recent work incomputationally modeling affective cognition, as well as future challenges for modeling
each of these inferences. Importantly, this unified framework allows us to describe all thereasoning in Table 1 using the same general principles (i.e., Bayesian inference) applied todifferent “components” of the causal model in Figure 1. In other words, how people reasonfrom outcomes to emotion, or infer emotion from expressions, can all be modeled with thesame domain-general inference machinery, under a common Bayesian “Theory of Emotion”(Ong, Zaki, & Goodman, 2015; Saxe & Houlihan, 2017).
Throughout the paper, we have posed affective cognition as a “computational level”
problem (Marr, 1982), and have focused on reviewing probabilistic approaches, which

EMOTION IN THEORY OF MIND

24

offer a natural solution to such inferential problems (e.g., Griffiths, Kemp, & Tenenbaum,
2008; Oaksford & Chater, 2007). The Bayesian approaches in the studies described here(de Melo et al, 2014; Ong, Zaki, & Goodman, 2015; Saxe & Houlihan, 2017; Wu et al, 2018)
share more commonalities than differences, and what differences exist lie mainly in which
variables the different sets of authors chose to prioritize or simplify out. Indeed, Figure 1
results from our efforts to unify the common ideas from these studies---for instance, every
study mentioned the crucial role of the third-person appraisal process and its causal link toemotion. We think that this computational Bayesian framework offers a principledapproach to unifying the inferences discussed, but it can also be supplemented byalternative, non-Bayesian approaches. For example, perhaps the complex expression-toemotion mapping might be best modeled with neural-network approaches (e.g., Schindler
et al, 2008). Additionally, process models and neuroscientific approaches (e.g., Adolphs,
2002) may shed more light on the "algorithmic" and "implementation" levels of analysis.
In our view, the biggest challenge ahead for models of affective cognition is finding
suitable computational representations, especially of emotions: What is the space ofemotions in the intuitive theory? Clearly, binary or multinomial (“angry” vs. not) labeling is
insufficiently comprehensive, although widely used in many classification tasks (likesentiment analysis). Should researchers then represent emotions in some high dimensional
space, and if so, what are those dimensions (Barrett & Russell, 1998; Mattek, Wolford, &Whalen, 2017)? How should mixed emotions be represented? Defining the representation
space is a crucial prerequisite for probabilistic modeling, enabling sampling from andmarginalizing over the space of emotions (as in Eqn. 3).

EMOTION IN THEORY OF MIND

25

But even a vector in some high-dimensional space may still be inadequate.
Intuitively, the three scenarios (a) “John is angry”, (b) “John is angry at receiving a negative
outcome”, and (c) “John is angry at the unfair process that led to the negative outcome”, areall qualitatively different because of the appraisal that resulted in the emotions, and thedifferent behavioral consequences they connote. This insight demands a richer, relational
representation of emotion that incorporates target- and event-related information(minimally, “angry_at_X”, “sad_because_Y”), which current Bayesian graphical models do
not support---although we think that modern incarnations like probabilistic programming
languages may offer a solution (e.g., Goodman, 2013, see also Goodman & Frank, 2016). In
our opinion, choosing a suitable representation for emotions (and appraisals) that captures
the richness of lay affective cognition and that can be computed over efficiently may prove
to be the largest hurdle to overcome.
Finally, we must stress that future work must prioritize modeling affective cognition
on naturalistic data. The sparse stimuli (e.g., static facial expressions) and experimental
scenarios in the studies discussed above are an important starting point, but they pale incomparison to the richness of everyday emotional experiences. It is important for future
research to model how laypeople reason about the emotions of others in naturalistic
contexts, such as watching someone in an unscripted monologue (e.g., Zaki, Bolger, &Ochsner, 2008; Devlin, Zaki, Ong, & Gruber, 2014, 2016) or dialogue (e.g., Ickes, Stinson,
Bissonnette, & Garcia, 1990). Modeling naturalistic contexts brings its own set ofchallenges---for example, extracting spontaneous emotional expressions and representing
the complex appraisals of naturalistic situations---but there is also great payoff. First, theyafford real-world tests of the validity of computational models developed on “clean”

EMOTION IN THEORY OF MIND

26

laboratory stimuli. Second, they will inform computational technologies that can reason
about their users’ emotions in a human-like manner (e.g., Picard, 1998).
In conclusion, we hope that the framework and taxonomy of inferences we present
here provides a useful conceptualization of work in computational models of affective
cognition. We have identified many important challenges that lie ahead for this nascentfield of research, which we are confident will be addressed by future researchers. At abroader level, our approach integrates well with state-of-the-art computational models inother domains of social cognition (Baker et al, 2017; Goodman et al, 2006; Goodman &Frank, 2016; Jara-Ettinger et al, 2016)---this integration will be crucial for a cumulative
science of social and affective reasoning.

EMOTION IN THEORY OF MIND

27
Acknowledgements

We thank Patricia Chen for feedback on multiple versions of this manuscript. This work
was supported in part by the A*STAR Human-Centric Artificial Intelligence Programme(SERC SSF Project No. A1718g0048), an A*STAR National Science Scholarship and a
Stanford IRiSS Computational Social Science Fellowship to DCO, NIH Grant
1R01MH112560-01 to JZ, and a DARPA PPAML Agreement number FA8750-14-2-0009 and
Sloan Foundation Research Fellowship to NDG.

EMOTION IN THEORY OF MIND

28
References

Adelson, E. H., & Bergen, J. R. (1991). The plenoptic function and the elements of earlyvision. In M. Landy and J. A. Movshon (eds), Computational Models of Visual
Processing (pp. 3-20). Cambridge, MA: MIT Press.
Adolphs, R. (2002). Recognizing emotion from facial expressions: psychological andneurological mechanisms. Behavioral and Cognitive Neuroscience Reviews, 1(1), 2162.
Alicke, M. D., Mandel, D. R., Hilton, D. J., Gerstenberg, T., & Lagnado, D. A. (2015). Causal
conceptions in social explanation and moral evaluation: A historical
tour. Perspectives on Psychological Science, 10(6), 790-812.
Arnold, M. B. (1960). Emotion and personality. New York: Columbia University Press.
Aviezer, H., Hassin, R. R., Ryan, J., Grady, C., Susskind, J., Anderson, A., Moscovitch, M., &Bentin, S. (2008). Angry, disgusted, or afraid? studies on the malleability of emotion
perception. Psychological Science, 19(7), 724–732.
Aviezer, H., Trope, Y., & Todorov, A. (2012). Body cues, not facial expressions, discriminate
between intense positive and negative emotions. Science, 338(6111), 1225-1229.
Baker, C. L., Saxe, R., & Tenenbaum, J. B. (2009). Action understanding as inverse
planning. Cognition, 113(3), 329-349.
Baker, C. L., Jara-Ettinger, J., Saxe, R., & Tenenbaum, J. B. (2017). Rational quantitative
attribution of beliefs, desires and percepts in human mentalizing. Nature Human
Behaviour, 1, 0064.
Banse, R., & Scherer, K. R. (1996). Acoustic profiles in vocal emotion expression. Journal of
Personality and Social Psychology, 70(3), 614.
Barrett, L., & Russell, J. A. (1998). Independence and bipolarity in the structure of current
affect. Journal of Personality and Social Psychology, 74(4), 967.
Beck, S. R., & Crilly, M. (2009). Is understanding regret dependent on developments incounterfactual thinking?. British Journal of Developmental Psychology, 27(2), 505510.
Böhm, G., & Pfister, H. R. (2015). How people explain their own and others’ behavior: atheory of lay causal explanations. Frontiers in Psychology, 6, 139.
Buck, R. (1994). Social and emotional functions in facial expression and communication:
The readout hypothesis. Biological Psychology, 38(2), 95–115.
Carey, S. (2009). The Origin of Concepts. Oxford University Press.
Carroll, J. M., & Russell, J. A. (1996). Do facial expressions signal specific emotions? Judging
emotion from the face in context. Journal of Personality and Social Psychology, 70(2),205.
Dael, N., Mortillaro, M., & Scherer, K. R. (2012). Emotion expression in body action andposture. Emotion, 12(5), 1085.
de Melo, C. M., Carnevale, P. J., Read, S. J., & Gratch, J. (2014). Reading people’s minds fromemotion expressions in interdependent decision making. Journal of Personality andSocial Psychology, 106(1), 73.
Delis, I., Chen, C., Jack, R. E., Garrod, O. G., Panzeri, S., & Schyns, P. G. (2016). Space-by-time
manifold representation of dynamic facial expressions for emotion
categorization. Journal of Vision, 16(8), 14-14.

EMOTION IN THEORY OF MIND

29

Devlin, H. C., Zaki, J., Ong, D. C., & Gruber, J. (2014). Not as good as you think? Trait positive
emotion is associated with increased self-reported empathy but decreased empathic
performance. PloS one, 9(10), e110470.
Devlin, H. C., Zaki, J., Ong, D. C., & Gruber, J. (2016). Tracking the emotional highs but
missing the lows: Hypomania risk is associated with positively biased empathic
inference. Cognitive Therapy and Research, 40(1), 72-79.
Ekman, P., Friesen, W. V., & Ellsworth, P. (1972). Emotion in the human face: Guide-lines forresearch and an integration of findings. New York: Pergamon Press.
Ekman, P., & Friesen, W. V. (1978). Facial Action Coding System. Palo Alto, CA: Consulting
Psychologists Press.
Elfenbein, H. A., & Ambady, N. (2002). On the universality and cultural specificity ofemotion recognition: a meta-analysis. Psychological Bulletin, 128(2), 203.
Ellsworth, P. C., & Scherer, K. R. (2003). Appraisal processes in emotion. In R. J. Davidson, H.
Goldsmith, & K. R. Scherer (Eds.), Handbook of Affective Sciences (pp. 572–595). New
York, NY: Oxford University Press.
Frank, M. C., & Goodman, N. D. (2012). Predicting pragmatic reasoning in language
games. Science, 336(6084), 998-998.
Frijda, N. H., Kuipers, P., & Ter Schure, E. (1989). Relations among emotion, appraisal, andemotional action readiness. Journal of Personality and Social Psychology, 57(2), 212.
Gendron, M., Roberson, D., van der Vyver, J. M., & Barrett, L. F. (2014). Perceptions ofemotion from facial expressions are not culturally universal: evidence from aremote culture. Emotion, 14(2), 251.
Gerstenberg, T. & Tenenbaum, J. B. (2017). Intuitive theories. In M. Waldmannn(Ed.), Oxford Handbook of Causal Reasoning (pp. 515-548). Oxford University Press.
Goodenough, F. L., & Tinker, M. A. (1931). The relative potency of facial expression andverbal description of stimulus in the judgment of emotion. Journal of Comparative
Psychology, 12(4), 365.
Goodman, N. D. (2013). The principles and practice of probabilistic programming. ACM
SIGPLAN Notices, 48(1), 399-402.
Goodman, N. D., Baker, C. L., Bonawitz, E. B., Mansinghka, V. K., Gopnik, A., Wellman, H.,
Schulz, L. & Tenenbaum, J. B. (2006). Intuitive theories of mind: A rational approach
to false belief. In Proceedings of the Twenty-Eighth Annual Conference of the Cognitive
Science Society (pp. 1382-1387).
Goodman, N. D., & Frank, M. C. (2016). Pragmatic language interpretation as probabilistic
inference. Trends in Cognitive Sciences, 20(11), 818-829.
Goodman, N. D., & Stuhlmüller, A. (2013). Knowledge and implicature: Modeling language
understanding as social cognition. Topics in Cognitive Science, 5(1), 173-184.
Gopnik, A., & Meltzoff, A. N. (1997). Words, thoughts, and theories. The MIT Press.
Griffiths, T. L. (2017). Formalizing prior knowledge in causal induction. In M. Waldmann,(Ed), The Oxford Handbook of Causal Reasoning. Oxford: Oxford University Press
Griffiths, T. L., Kemp, C., & Tenenbaum, J. B. (2008). Bayesian models of cognition. In Ron
Sun (ed.), The Cambridge Handbook of Computational Cognitive Modeling. Cambridge
University Press.
Griffiths, T. L., & Tenenbaum, J. B. (2006). Optimal predictions in everyday
cognition. Psychological Science, 17(9), 767-773.

EMOTION IN THEORY OF MIND

30

Gross, A. L., & Ballif, B. (1991). Children's understanding of emotion from facial expressions
and situations: A review. Developmental Review, 11(4), 368-398.
Halpern, J. Y., & Pearl, J. (2005). Causes and explanations: A structural-model approach.
Part II: Explanations. The British Journal for the Philosophy of Science, 56(4), 889911.
Hareli, S., & Hess, U. (2010). What emotional reactions can tell us about the nature ofothers: An appraisal perspective on person perception. Cognition andEmotion, 24(1), 128-140.
Harris, P. L. (1989). Children and emotion: The development of psychological understanding.
Basil Blackwell.
Heider, F. (1958). The psychology of interpersonal relations. New York: Wiley.
Ickes, W., Stinson, L., Bissonnette, V., & Garcia, S. (1990). Naturalistic social cognition:
Empathic accuracy in mixed-sex dyads. Journal of Personality and Social
Psychology, 59(4), 730.
Isen, A. M. (1987). Positive affect, cognitive processes, and social behavior. Advances inExperimental Social Psychology, 20, 203-253.
Jack, R. E., Blais, C., Scheepers, C., Schyns, P. G., & Caldara, R. (2009). Cultural confusions
show that facial expressions are not universal. Current Biology, 19(18), 1543-1548.
Jack, R. E., Caldara, R., & Schyns, P. G. (2012). Internal representations reveal cultural
diversity in expectations of facial expressions of emotion. Journal of Experimental
Psychology: General, 141(1), 19.
Jara-Ettinger, J., Gweon, H., Schulz, L. E., & Tenenbaum, J. B. (2016). The naïve utility
calculus: computational principles underlying commonsense psychology. Trends in
Cognitive Sciences, 20(8), 589-604.
Jern, A., & Kemp, C. (2015). A decision network account of reasoning about other people’s
choices. Cognition, 142, 12-38.
Johnstone, T., & Scherer, K. R. (2000). Vocal communication of emotion. Handbook of
Emotions, 2, 220-235.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk.
Econometrica, 47(2), 263–292.
Kahneman, D., & Tversky, A. (1982). The simulation heuristic. In D. Kahneman, P. Slovic, &A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (p. 201- 208).
Cambridge University Press
Kemp, C., & Jern, A. (2014). A taxonomy of inductive problems. Psychonomic Bulletin &Review, 21(1), 23-46.
Kermer, D. A., Driver-Linn, E., Wilson, T. D., & Gilbert, D. T. (2006). Loss aversion is anaffective forecasting error. Psychological Science, 17(8), 649-653.
Koller, D., & Friedman, N. (2009). Probabilistic graphical models: principles and techniques.
MIT press.
Krumhuber, E., Manstead, A. S., Cosker, D., Marshall, D., Rosin, P. L., & Kappas, A. (2007).
Facial dynamics as indicators of trustworthiness and cooperative
behavior. Emotion, 7(4), 730.
Lagattuta, K. H., Wellman, H. M., & Flavell, J. H. (1997). Preschoolers' understanding of thelink between thinking and feeling: Cognitive cuing and emotional change. Child
Development, 68(6), 1081-1104.

EMOTION IN THEORY OF MIND

31

Lagnado, D. A., Gerstenberg, T., & Zultan, R. I. (2013). Causal responsibility andcounterfactuals. Cognitive Science, 37(6), 1036-1073.
Loewenstein, G., & Lerner, J. S. (2003). The role of affect in decision making. Handbook of
Affective Science, 619(642), 3.
Lerner, J. S., Li, Y., Valdesolo, P., & Kassam, K. S. (2015). Emotion and decision
making. Annual Review of Psychology, 66, 799-823.
Levine, E. E., Barasch, A., Rand, D. G., Berman, J. Z., & Small, D. A. (2018). Signaling Emotion
and Reason in Cooperation. Journal of Experimental Psychology: General, 147(5),702.
Lucas, C. G., & Kemp, C. (2015). An improved probabilistic account of counterfactual
reasoning. Psychological Review. 122(4), 700-734.
Malle, B. F. (1999). How people explain behavior: A new theoretical framework. Personality
and Social Psychology Review, 3(1), 23–48.
Malle, B. F. (2011). Attribution theories: How people make sense of behavior. In Theories in
Social Psychology (pp. 72–95). Wiley-Blackwell Malden, MA.
Marr, D. (1982). Vision. San Francisco: W. H. Freeman.
Martinez, A., & Du, S. (2012). A model of the perception of facial expressions of emotion byhumans: Research overview and perspectives. Journal of Machine Learning
Research, 13, 1589-1608.
Mattek, A. M., Wolford, G. L., & Whalen, P. J. (2017). A mathematical model captures the
structure of subjective affect. Perspectives on Psychological Science, 12(3), 508-526.
Mellers, B. A., Schwartz, A., Ho, K., & Ritov, I. (1997). Decision affect theory: Emotional
reactions to the outcomes of risky options. Psychological Science, 8(6), 423-429.
Moors, A., Ellsworth, P. C., Scherer, K. R., & Frijda, N. H. (2013). Appraisal theories of
emotion: State of the art and future development. Emotion Review, 5(2), 119-124.
Oaksford, M., & Chater, N. (2007). Bayesian rationality: The probabilistic approach to humanreasoning. Oxford University Press, USA.
Oaksford, M., & Chater, N. (2010). Causation and conditionals in the cognitive science ofhuman reasoning. Open Psychology Journal, 3, 105–118.
Ong, D. C., Asaba, M., & Gweon, H. (2016). Young children and adults integrate past
expectations and current outcomes to reason about others' emotions. In Proceedingsof the 38th Annual Meeting of the Cognitive Science Society, 135-140.
Ong, D. C., Goodman, N. D., & Zaki, J. (2015). Near-misses sting even when they are
uncontrollable. In Proceedings of the 37th Annual Meeting of the Cognitive Science
Society, 1775-1780.
Ong, D. C., Zaki, J., & Goodman, N. D. (2015). Affective cognition: Exploring lay theories of
emotion. Cognition, 143, 141-162.
Ong, D. C., Zaki, J. & Goodman, N. D. (2016). Emotions in lay explanations of
behavior. Proceedings of the 38th Annual Meeting of the Cognitive Science Society,360-365.
Ortony, A., Clore, G. L., & Collins, A. (1988). The cognitive structure of emotions. New York:
Cambridge University Press.
Pearl, J. (2001). Direct and indirect effects. In Proceedings of the Seventeenth Conference on
Uncertainty in Artificial Intelligence, 411-420.
Pearl, J. (2009). Causality: Models, Reasoning, and Inference. Cambridge University Press.

EMOTION IN THEORY OF MIND

32

Repacholi, B. M., & Gopnik, A. (1997). Early reasoning about desires: evidence from 14-and
18-month-olds. Developmental Psychology, 33(1), 12.
Repacholi, B. M., Meltzoff, A. N., Hennings, T. M., & Ruba, A. L. (2016). Transfer of Social
Learning Across Contexts: Exploring Infants' Attribution of Trait-Like Emotions to
Adults. Infancy, 21, 785--806. doi:10.1111/infa.12136
Ross, L. (1977). The intuitive psychologist and his shortcomings: Distortions in theattribution process. Advances in Experimental Social Psychology, 10, 173-220.
Russell, J. A. (1994). Is there universal recognition of emotion from facial expression? A
review of the cross-cultural studies. Psychological Bulletin, 115(1), 102.
Russell, J. A., Bachorowski, J. A., & Fernández-Dols, J. M. (2003). Facial and vocal
expressions of emotion. Annual Review of Psychology, 54(1), 329-349.
Saxe, R., & Houlihan, S. D. (2017). Formalizing emotion concepts within a Bayesian model oftheory of mind. Current Opinion in Psychology.
Scherer, K. R. (2003). Vocal communication of emotion: A review of researchparadigms. Speech Communication, 40(1), 227-256.
Scherer, K. R., & Grandjean, D. (2008). Facial expressions allow inference of both emotions
and their components. Cognition and Emotion, 22(5), 789-801.
Schindler, K., Van Gool, L., & de Gelder, B. (2008). Recognizing emotions expressed by bodypose: A biologically inspired neural model. Neural Networks, 21(9), 1238-1246.
Skerry, A. E., & Saxe, R. (2014). A common neural code for perceived and inferred emotion.
Journal of Neuroscience, 34(48), 15997-16008.
Skerry, A. E., & Saxe, R. (2015). Neural representations of emotion are organized aroundabstract event features. Current Biology, 25(15), 1945-1954.
Skerry, A. E., & Spelke, E. S. (2014). Preverbal infants identify emotional reactions that areincongruent with goal outcomes. Cognition, 130(2), 204-216.
Smith, C. A., & Lazarus, R. S. (1993). Appraisal components, core relational themes, and theemotions. Cognition & Emotion, 7(3-4), 233-269.
Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning: An introduction. Cambridge: MITpress.
Van Kleef, G. A., De Dreu, C. K., & Manstead, A. S. (2010). An interpersonal approach toemotion in social decision making: The emotions as social information
model. Advances in Experimental Social Psychology, 42, 45-96.
Wellman, H. M., & Banerjee, M. (1991). Mind and emotion: Children's understanding of theemotional consequences of beliefs and desires. British Journal of Developmental
Psychology, 9(2), 191-214.
Wellman, H. M., & Bartsch, K. (1988). Young children’s reasoning about beliefs. Cognition,30(3), 239-277.
Wellman, H. M., & Gelman, S. A. (1992). Cognitive development: Foundational theories ofcore domains. Annual Review of Psychology, 43(1), 337-375.
Wellman, H. M., Phillips, A. T., & Rodriguez, T. (2000). Young children's understanding ofperception, desire, and emotion. Child development, 71(4), 895-912.
Wenzler, S., Levine, S., van Dick, R., Oertel-Knöchel, V., & Aviezer, H. (2016). Beyond
pleasure and pain: Facial expression ambiguity in adults and children during intense
situations. Emotion, 16(6), 807-814.
Wondra, J. D., & Ellsworth, P. C. (2015). An appraisal theory of empathy and other vicarious
emotional experiences. Psychological Review, 122(3), 411.

EMOTION IN THEORY OF MIND

33

Wu, Y., Baker, C. L., Tenenbaum, J. B., & Schulz, L. (2018). Rational inference of beliefs anddesires from emotional expressions. Cognitive Science. 42:850884. doi:10.1111/cogs.12548
Wu, Y., Muentener, P., & Schulz, L. (2017). One- to four-year-olds connect diverse positive
emotional vocalizations to their probable causes. Proceedings of the National
Academy of Sciences. doi:10.1073/pnas.1707715114
Wu, Y., & Schulz, L. (2017). Inferring beliefs and desires from emotional reactions toanticipated and observed events. Child Development. doi:10.1111/cdev.12759
Yuki, M., Maddux, W. W., & Masuda, T. (2007). Are the windows to the soul the same in the
East and West? Cultural differences in using the eyes and mouth as cues to recognize
emotions in Japan and the United States. Journal of Experimental Social
Psychology, 43(2), 303-311.
Zaki, J., Bolger, N., & Ochsner, K. (2008). It takes two: The interpersonal nature of empathic
accuracy. Psychological Science, 19(4), 399-404.
Zaki, J., & Ochsner, K. (2011). Reintegrating accuracy into the study of social cognition(Target Article). Psychological Inquiry, 22(3), 159-182.