2.1 Denotative and Connotative Meaning

According to the social psychological framework of symbolic interactionism, people base their decisions and actions on culturally shared meanings of things, which have evolved and are maintained and constantly reproduced in social interaction (Reference Berger and LuckmannBerger & Luckmann, 1967; Reference BlumerBlumer, 1969; Reference MeadMead, 1934). When socialized in a given culture, people internalize semantic structures that serve as default frames to keep their individual decisions more or less in line with social expectations. A socially embedded formal model of decision making needs to operationalize such meaning structures, which is precisely what BayesACT does. Influenced by debates in philosophy and linguistics about the distinction between denotative (precise, propositional, definitional) and connotative (vague, associative, intuitive) meanings of words for objects and events, Reference Osgood, Suci and TannenbaumOsgood et al. (1957, 1975) developed the semantic differential as a method for quantifying so-called “affective meanings”, which were later shown to be highly consensual within linguistic communities (Reference Ambrasat, von Scheve, Conrad, Schauenburg and SchröderAmbrasat et al., 2014; Reference HeiseHeise, 2010). These affective meanings serve in our BayesACT model of decision-making as a basis for a deep, intuitive layer that aligns individual decision makers with their cultural environment, while also allowing a more detached decision theoretic mode, thus avoiding the oversocialization problem.

The distinction between a connotative, socialized and a denotative, individualized process of decision making calls to memory the cognition-versus-affect debate because dual process models based on that dichotomy raise the question of the relation between these two modes of psychological experience. This is a perennial issue in psychology that reaches back almost a hundred years to the James-Lange (Reference Lange and JamesLange & James, 1922) proposal that emotional experience is simply our (cognitive) perception of physiological arousal that has already occurred in response to external stimuli (e.g. we feel scared because we run, and feel happy because we smile). After a long period of relative dormancy, the issue re-surfaced in the 1980s as the primacy of cognition-versus-affect debate between Reference ZajoncZajonc (1980, 1984) and Reference LazarusLazarus (1984); and continues to be a controversial subject in contemporary psychology, as evidenced by special issues of journals devoted to the topic (e.g., Reference Mather and FanselowMather & Fanselow, 2018).

Although evidence from neuroscience does not support a clear distinction between cognition and affect at the neurobiological level of the brain, there is a general consensus that the distinction holds at the psychological (experiential, phenomenological) level of the mind, e.g., (Reference Duncan and BarrettDuncan & Barrett, 2007; Reference Barrett and SatputeBarrett & Satpute, 2013). At this level, the relation between cognition and affect can be expressed by two principles (Reference MacKinnonMacKinnon, 1994). According to the principle of inextricability, cognition and affect are overlapping constituents or processes of the mind but analytically and empirically distinct as well. To expound, the relation between cognition and affect can be best viewed as a continuum between the extremes of “cold” cognitions where the intensity of affective arousal is low and “hot” cognitions where arousal is quite pronounced; or, alternatively, at the extremes of affective experience largely unmediated by cognitive processing and that involving a high level of cognitive appraisal and reaction. According to the principle of complementarity, to the extent that cognition and affect are at least partially independent systems, both are required for an adequate understanding of the human mind. While the principle of inextricability is an ontological statement about the reality of the mind as we understand it, the principle of complementarity is an epistemological implication of this understanding. Finally, we believe that the debate over the relative primacy of cognition and affect largely dissolves if their relation is viewed as a reciprocal process, as suggested by many authors (e.g., Reference MookMook, 1987; Reference ForgasForgas, 2008). An interdisciplinary overview of the relationships between these different strands of research can be found in Reference MacKinnon and HoeyMacKinnon & Hoey (2021).

2.2 Affect Control Theory

The reciprocal relationship between cognition and affect is a core assumption of Affect Control Theory (ACT) (Reference HeiseHeise, 2007; Reference MacKinnonMacKinnon, 1994), which capitalizes on the three-dimensional model of affective meaning established by Reference Osgood, Suci and TannenbaumOsgood et al. (1957, 1975). Comprising feelings of evaluation, potency, and activity (EPA), the dimensional simplicity of connotative-affective meaning provides a portal into the dimensionally complex denotative-cognitive representations of the world. Affective reactions to external objects and stimuli become “the means by which information about the external world is translated into an internal code or representation that can be used to safely navigate the world” (Reference Duncan and BarrettDuncan & Barrett, 2007, p. 1186). For example, a person wearing a lab coat in a hospital setting would lead to a denotative impression of this person that is represented with a symbol (doctor). This symbol has an associated fundamental sentiment in a three-dimensional affective EPA space of evaluation (E: good/bad), power (P: strong/weak) and activity (A: active/inactive). Doctors are usually associated with feelings of positive valence and positive power. EPA space has been found through decades of research to be a cross-culturally normative representation of connotative meaning (Reference OsgoodOsgood, 1969).

Population surveys on semantic differential scales (with opposing adjectives at each end) provide a link from denotative to connotative as a set of samples from a distribution in sentiment space. A parametric representation can be computed (e.g. as the mean and variance of a normal distribution), or a non-parametric representation used (e.g. a set of samples). Parametric representations have been compiled in “dictionaries” of mappings from labels to sentiment. These dictionaries typically only code the mean of a distribution, and filtering operations are used to remove data that is not distributed normally. Thus, in ACT, a doctor is represented connotatively as (EPA:{2.7,3.0,0.23}).Footnote ³ A denotative label can be assigned to a connotative (EPA) vector in ACT using a simple nearest neighbour method (e.g. the closest label to (EPA:{1.5,−0.50,−2.0}) is librarian (EPA:{2.0,−0.46,−2.1}) - at a Euclidean distance of 0.017).

These surveys also yield equations for in-context impression formation. For example, participants are asked about specific actor-behavior-object (ABO) situations, e.g., librarian reprimand (EPA:{−0.36,1.7,1.0}) bookworm (EPA:{1.6,0.41,−2.4}), and asked to rate each element. The basic premise of ACT is that such situations are assessed as a single unit in the connotative space, called a “transient impression”. The difference between this transient impression and the out-of-context estimates (fundamental sentiments), used as an optimization loss, guides agents’ actions or reinterpretations of the situation to reduce emotional incoherence. This emotional incoherence is called “deflection” in ACT. In BayesACT, there is additional incoherence in the denotative state, termed ambiguity (see Section 2.3).

The difference between fundamental sentiments and transient impressions is modeled using a set of polynomial features that multiply together aspects of the situation to yield a final estimate of the transient meanings. For example, a positively weighted polynomial term in the equation for the transient impression of an actor’s evaluation multiplies the actor’s fundamental evaluation score with the selected behavior’s evaluation, and represents the fact that good people normally do good things. Other factors represent balance effects (good actors can do bad things to bad actors), and other elements of emotional coherence. The number of factors is empirically determined (Reference HeiseHeise, 2010).

In the bookworm example, the librarian, having performed a negative and powerful behavior, results in him feeling more bad and more powerful (EPA:{−1.0,1.9,3.1}) with closest label hot shot (EPA:{−1.0,1.1,2.5}), while the bookworm would feel more bad and more active (EPA:{−1.2,0.30,−0.10}) with closest label truant (EPA:{−0.73,−0.08,0.40}).Footnote ⁴ Each agent can either re-identify the other or the self (as truant and hot shot), or can take action to resolve incoherence. The optimal action in this case (in the sense of reducing incoherence) is to seek advice from (EPA:{2.1,1.1,−0.34}) for the librarian and to assist (EPA:{3.3,2.6,0.56}) for the bookworm.

The surveys conducted under the ACT paradigm also yield the impressions of adjective-noun combinations. That is, identities can be “modified” by adjectives, and so a doctor who is frustrated (EPA:{−2.0,−0.34,1.2}) will have a different emotional signature from a doctor (frustrated doctor EPA:{−1.1,1.6,0.70}). The effects of these modifiers are also determined through population surveys of modifier words. Other components of ACT may include settings (e.g. doctor in a hospital vs. doctor at home).

Emotions in ACT are defined as the vector difference between the fundamental (out-of-context) sentiments about a person and the transient (in-context) impressions formed as a result of an event. Emotions are a mechanism to help agents signal (in)coherence to each other (e.g. with facial expressions or paralinguistics). Importantly, these signals are not scalar indications of (in)coherence, but rather vector signals causing intuitive decisions about appropriate restorative behavior. For example, if a doctor talks down to (EPA:{−1.6,−0.07,0.31}) another doctor, the object agent is made to feel less powerful than expected (drops to −0.1), and will display exasperation or indignance. Upon receiving this signal, the acting agent may restore fundamental sentiments by making up with the other. Identities have “characteristic emotions” which are those felt when agents are in a perfectly coherent environment, or one that is responding exactly according to their world model. For example, a doctor has a characteristic emotion (EPA:{2.0,0.90,0.0}), with closest labels of captivated or agreeable, while for a delinquent it is (EPA:{−2.0,−0.70,0.075}), with closest label inconsiderate.

Lastly, the mean sentiments recorded in dictionaries are empirical estimates of the distribution of the individually reported sentiment in the population studied. Thus, one would expect that measurements of these sentiments over more diverse populations would have larger variances. However, we are using these distributions as models of individual reasoning in this paper. This is reasonable given the assumption that the human mind is a model of the system it is embedded in (the “good regulator” theorem (Reference Conant and AshbyConant & Ashby, 1970)), and thus represents the diversity in the population as a distribution in its own model with a matching variance. Another way to see this is by noticing that a person interacting with its world will “sample” the sentiments of the network(s) in which it is embedded, and estimate the mean and variance of the sentiment in much the same way as we estimate these numbers from population surveys. Agents embedded in novel networks will potentially need to adjust their estimates in order to better “fit” the group.

2.3 BayesACT

Extending ACT, BayesACT is a computational dual process model of intelligence (Reference Hoey, Schröder and AlhothaliHoey et al., 2016; Reference Schröder, Hoey and RogersSchröder et al., 2016). One process (connotative) is continuous in a space spanning one or more dimensions and is equated with sentiment or affect, while the other (denotative) is defined on a discrete and high dimensional space and models logical and production-rule based reasoning. The connotative process is a probabilistic generalization of the emotional-coherence mechanism of ACT explained in the previous section, treating EPA meanings as probability distributions rather than point estimates and thus allowing uncertainty or individual variability. The dual process is built to handle uncertainty and surprise. It naturally shifts between higher bias models (lower variance in the connotative space) in more denotatively uncertain (invalid/unpredictable/surprising) situations, to lower bias models (higher precision in the denotative space) in more denotatively certain (valid/predictable/unsurprising) environments.

2.3.2 Mathematical Model

BayesACT is a Bayesian decision network known as a partially observable Markov decision process (POMDP), a formal model with precise probabilistic and decision theoretic semantics (Reference ÅströmÅström, 1965; Reference PutermanPuterman, 1994; Reference Kaelbling, Littman and CassandraKaelbling et al., 1998; Reference Boutilier, Dean and HanksBoutilier et al., 1999). In the following, we use standard notation where capital letters denote random variables, small letters represent values those variables can take on, and bold letters represent sets of variables or values. Thus, X is a set of random variables, X is a single random variable, x is a particular value for all variables in the set X and x is a particular value that variable X can take on. Capital letters in calligraphic script, X, denote the space spanned by a variable or set of variables.

We start with the assumption that an agent must maintain an internal model of the world as a set of states making up a state space S, which is factored into a denotative part, X, that describes the ontological states of entities in the world, and a connotative part, Y, that describes the affective meanings of entities in the world. In ACT and BayesACT, the connotative space spans the three-dimensional vector space of EPA sentiments for identities (labels assigned to people) and behaviors (labels assigned to people’s actions). The denotative space is discrete and factored, and contains representations of each actor’s identity (as a label). For example, a particular agent’s identity may be represented by some X, such that the word doctor in the English language is a particular value of that variable X = doctor. Similarly, Y = y will represent the affective meaning (in EPA space) of that denotative entity.Footnote ⁶

BayesACT has two random variables corresponding to observations, Ω = {Ω_x,Ω_e}. One, Ω_x, represents signals about the environment giving evidence for the denotative state. The other, Ω_e, represents emotional signals from other agents, and gives direct evidence for the connotative state. Information flows into the model from both connotative and denotative sides, and BayesACT computes posterior distributions that best merge the two in a Bayesian sense. Emotion signals are crucial for grounding the connotative state, as otherwise it could be arbitrarily transformed between agents and would be harder to learn. Finally, BayesACT has two sets of actions representing denotative action, A, and connotative meanings of those actions, F_b.Footnote ⁷

Figure 1 shows a graphical model representation of BayesACT.Footnote ⁸ This graphical model shows random variables as circles, decision variables (under the control of the agent) as squares.Footnote ⁹ Undirected (directed) links give probabilistic (conditional) dependencies between variables. Thus, an undirected link between X and Y represents P(X,Y), while X → Y represents P(Y|X).

Figure 1:

Bayesian decision network for BayesACT at a high level of abstraction showing denotative X and connotative Y, observations Ω_x, emotions Ω_e, and actions both denotative A, and connotative F_b. Directed links imply (but do not require) causality as in a Bayesian network. Two somatic potentials, modeled as undirected links (see text), link state and action, respectively. Primed variables are post-event, and the network is dynamically unrolled through time.

The graphical model is defined for a discrete temporal sequence, with one set of variables for each time step. Two time slices are shown in Figure 1, with primed variables indicating those that are in existence after an action is taken, but in reality the network is “unrolled” for as many time steps as required, and the dynamics is considered stationary (does not change over time).Footnote ¹⁰ A Bayesian decision network, along with associated probabilities and utility functions, can be used to answer queries of the form , the posterior distribution over the denotative state at time t given observations up to that time of Ω₀,Ω₁,…,Ω_t. A number of algorithms exist for computing these inferences, and these can be computed efficiently and recursively for structured models such as a POMDP by repeatedly taking products and sums of conditional probability and utility functions. Optimal decisions can also be computed using similar algorithms, where maximization over the action variables takes place of summations for random variables. However, these computations are significantly more difficult than those for inference, and normally require approximations such as stochastic simulation (Monte-Carlo tree search), or variational inference, see (Reference Hoey, Schröder and AlhothaliHoey et al., 2016; Reference Asghar and HoeyAsghar & Hoey, 2015; Reference Silver, Veness, Lafferty, Williams, Shawe-Taylor, Zemel and CulottaSilver & Veness, 2010).

BayesACT is formally specified (as a dynamic decision network) and makes clear predictions about tradeoffs between making decisions based on affective identity and expected utility. It therefore has a clear specification and empirical content (Reference Glöckner and BetschGlöckner & Betsch, 2011). Further, it is falsifiable as identity can be modified as an independent variable to make different predictions with different experimental setups (see Section 5.3). In high certainty conditions, we expect decisions to be largely independent of identity, so BayesACT predictions would be largely in agreement with parallel constraint network models. In low certainty conditions (high ambiguity), we expect the predictions of the two models to diverge, but we expect the BayesACT predictions to be more precise due to its ability to specialize based on this additional context.

3.1 The Somatic Transform

A core element in the BayesACT POMDP is that every denotative element X (including agent actions, A) has an associated connotative element Y (F_b for behaviours). The connection between denotative and connotative elements is written as a functional called the somatic transform: Ĝ(X, Y). The somatic transform specifies the shared cultural connotative interpretation of the denotative state X. That is, for some x, Ĝ(x,Y) is a function over the connotative space, Y, representing the shared sentiments for denotative state x. For example, Ĝ(X_a = doctor,Y) could be a normal distribution given by summary statistics (mean, covariance) measured in a population survey. Using a somatic transform, agents can interoceptively ask questions such as “what do I feel about object x?” (e.g., Q: “how do you feel about doctors?”; A: “I see doctors as quite good, quite powerful, and a bit active, but I’m somewhat uncertain about this”).

The somatic transform can also yield, for some y, a function over the denotative space, X, Ĝ(X,y). For some discrete set of N denotative entities, X = {x₁,x₂…x_N}, this could be a multinomial distribution (a set of numbers p ₁,p ₂,…p _N such that 0≤ p _i ≤ 1 ∀ i and indicating that entity x_i is likely with probability p _i. Such a distribution can be computed using, e.g., a kernel method. The agent can therefore also ask questions such as “what sort of x feels like y?” (e.g., Q: ”what sort of things are very good, a bit weak, and very active?”; A: “dogs, smiley faces, kids”).

To give the somatic transform a more precise definition, we may model it as a joint probability distribution over X and Y, written as a Boltzmann distributionFootnote ¹¹ of the somatic potential, which we write as E(x,y), denoting the energy or incoherence between the denotative and connotative states:

(1)

where M(X = x) is a function in Y giving the connotative value for that particular x and c is a normalizing constant (the inverse of the partition function). M may be simply the mean of the population survey for the concept X = x, and γ a constant. Thus, the more coherent x is with y, the smaller the energy , and the more likely the state. The parameter γ models one aspect of the (affective) predictability of the environment. As the environment’s diversity increases (say with the addition of some heterogeneous other agents), γ naturally increases as the ascription of sentiment to denotative elements in the world is less well defined. Such a world becomes less predictable and less valid both connotatively (sentiment less well defined) and denotatively (heterogeneous agents behaving in different ways). A value for γ is a learning choice to be made by an agent. Although we know that γ is related to the variance in sentiments in the population, it does not need to be exactly the same. The value of γ will also be a function of the agent’s social network, as the agent may operate in a clique or cluster of locally more homogeneous sentiments.

Here, we suppose that a prior marginal over X, P(x), represents the agent’s current estimate of the denotative nature of the interaction. It can be a belief about various properties of objects being manipulated as part of the ongoing interaction, for example. Thus, an agent may observe a female in a white coat in a hospital setting, and infer a distribution over the possible identities of nurse or doctor. In this case, an agent with a gender stereotype may form a denotative impression which puts more mass on nurse than on doctor.Footnote ¹² The result of the inference is P(x), and would be represented in this simple case with one marginal number p giving the probability that this entity (person) is a nurse, for a distribution over [nurse, doctor] of Footnote ¹³

Suppose further that a prior marginal distribution over Y, P(y), represents an agent’s current estimate of the affective nature of the interaction. It can be a belief about identity sentiments of participants, recent or forthcoming behavior sentiments, or sentiments about settings or other physical objects. Suppose the agent had observed the same female in the white coat performing a gesture implying she has power, such as ordering someone to do something. In this case, the agent’s prior over the sentiment about the white-coated female, Y, would be shifted towards more powerful values which might conflict with denotative bias.

Using a joint prior that is factored as P(X,Y) = P(X)P(Y), we seek a posterior distribution P ^′(X,Y) = P(X^′,Y^′) that combines priors with the constraint imposed by the somatic transform (Equation 1). We write both distributions and density functions as P(·), as the type of function and operations used is defined by the variable in context X or Y. As we are focussing on the somatic transform only, we ignore the temporal dynamics (explored more fully in Reference Hoey, Schröder and AlhothaliHoey et al. (2016)), and so consider primed and unprimed variables to be the same (so the prior over unprimed variables becomes the prior over primed variables). We further ignore the observation spaces Ω_x and Ω_e, simply integrating probability weights into priors over X^′ and Y^′, respectively. In fact, we are seeking the posterior given our knowledge of Equation 1. We postulate a variable G representing our knowledge that a somatic transform such as Equation 1 connects denotative (X) and connotative (Y) spaces. We therefore write that

(2)

and we see that the joint distribution is in fact a product of the somatic transform and the posterior distribution (which may be factored into two distributions over X^′ and Y^′). In the one-dimensional case, with a somatic transform defined to be the Boltzmann distribution as above, and factored priors P(x) and P(y), an estimate of the marginal posterior over Y (P ^′(y), the feelings evoked after an event) can be computed as:

(3)

where the ∝ shows the quantities are proportional (equal up to a constant multiplier, labeled c in Equation 1). Thus, the posterior distribution over Y is the expectation of the somatic transform with respect to the prior distribution over X, P(x), multiplied by the prior distribution over Y.

Similarly, the marginal posterior distribution over X, P ^′(x), is given by

(4)

The posterior distribution over X is the expectation of the somatic transform with respect to the prior distribution over Y, P(y), multiplied by the prior distribution over X.

Equations 3 and 4 can be analytically computed in the case of Gaussian priors, which we pursue below. In practice, the somatic transform can be problematic because it generates a posterior over Y which is no longer a single Gaussian, but a sum of Gaussians. Projecting this very far into the future may lead to an explosion of modes. However, modes can be combined or rejected by action selection as well, meaning that for each sum of Gaussians generated, one can be selected through action. In the doctor example, a sum of two Gaussians results after a single iteration but the act of deference performed can resolve much of this uncertainty by committing to one hypothesis or the other. Further, there are analytical methods for handling the explosion of modes, such as Bayesian moment matching (Reference Jaini and PoupartJaini & Poupart, 2016). Finally, higher level models at the institutional or self level may help through regularization (damping) of learning (Reference MacKinnon and HeiseMacKinnon & Heise, 2010; Reference HoeyHoey & Schröder, 2015).

3.2 Relationship of BayesACT and ACT

In Affect Control Theory (ACT), the somatic transform has a zero temperature parameter γ=0. Further, either P(x) is a point estimate (x _o), and P(y) is a constant (no prior, set to 1), or P(y) is a point estimate (y _o) and P(x) is a constant. Writing a point estimate as a delta function, δ(x − x _o), where δ(x − x _o )=1 if x =x _o and 0 otherwise, then in the first case, Equation 3 is:

(5)

and in the second case, Equation 4 is:

(6)

which simply says that x _o and y _o are related through the function M directly (e.g. M is a dictionary linking each x _o with a y _o). Technically in Equation 6 this assumes a dictionary with an entry for every possible y _o, clearly an impossibility. Finding the nearest neighbor, as described above, is one possible way to circumvent this.

As mentioned previously, the somatic transform is the key difference between our presentation of the model here and the presentation of it in the original exposition of the BayesACT model (Reference Hoey, Schröder and AlhothaliHoey et al., 2016; Reference Schröder, Hoey and RogersSchröder et al., 2016). In the original presentation, we assumed that behaviors were both perceived and generated in the connotative/affective-space, leaving the translation to/from denotative spaces to some other perceptual or motor system. The somatic transform mathematically defines this translation and integrates it directly and deeply into the model itself. Rather than perceiving a behavior as a vector in a 3D affective space, an agent perceives and cognitively interprets denotative aspects of the situation including behavior, then uses these denotative aspects as evidence in support of its connotative/affective predictions, computing the level of support using a somatic transform. Simultaneously, connotative predictions are mapped to future denotative states and actions, providing heuristic guidance to an agent. This aspect of the original presentation of the BayesACT model is thus revealed as a simplifying assumption that has been replaced here with the more general somatic transform.

3.3 Somatic Transform Examples

Figure 2 shows an example usage of this transform for the simple case discussed previously. In it, we consider a prior over y, P(y), as a Gaussian distribution with a variance σ_y = 2.0 and a mean u _y which is varied to see the effect of a changing connotative prior. These distributions are shown as dashed lines in Figure 2 (with means ranging from −1 to 5). A prior over x, P(x), represents only two identities nurse and doctor with probabilities 0.7 (nurse) and 0.3 (doctor). A-priori, the agent believes it is more likely this person is a nurse. The somatic transform is implemented using normal distributions as the values of M mapping a label in X to a mean and variance in Y given by suurvey data generated at the University of Georgia in 2015. The identities of nurse and doctor have power (P) values of 1.9 and 3.0, respectively. We only consider a single dimension here for ease of exposition, but the results carry over to 3 (or, in principle, more) dimensions. In Figure 2, we use γ=0.3, but investigate how γ affects the results in Figure 3.

Figure 2:

Effects of the somatic transform on the posterior marginals over X and Y. (a) Gaussian priors over Y are shown as dashed lines for different values of µ_y. The prior over X is P(X = nurse)=0.7. The posterior over Y is shown as solid lines, while the posterior over X is shown in the legend, with S(P ^′) denoting the entropy of P ^′(X) and P ^′(nurse) denoting P ^′(X = nurse). As the prior shifts to more positive values in Y, the posterior in Y shifts to be more in line with the power sentiment about doctor, rather than nurse. Further, the posterior in X also favors doctor (that is, P ^′(nurse)→ 0.0). (b) plot of the overall trends in entropy and posterior probability as a function of µ_y.

Figure 3:

Posterior over Y with varying γ. (a) As γ decreases, the posterior over Y is more focussed on the priors over x. S(P ^′) denotes the entropy of P ^′(X). P ^′(nurse) denotes the posterior probability of X being nurse: P ^′(X = nurse). Prior in Y is µ_y = 3.0,σ_y = 2.0. (b) plot of the overall trends in entropy and posterior probability as a function of γ. Note the different scale in (b) to Figure 2.

Figure 2(a) shows how the posteriors evolve as µ_y is changed. The entropy in the posterior distribution over x, P ^′(x), is shown as S(P ^′) in the legend and in Figure 2(b), along with the value of P ^′(X = nurse) as P ^′(nurse). The posteriors over y, P ^′(y) are shown as solid lines. First, we can see that as the prior over y approaches the prior over x (with an expected Power sentiment value of 0.7× 1.9+0.3× 2.95 = 2.2), the posterior becomes a bimodal distribution with about 70% of its mass nearer to the nurse identity at 1.9. Further, as the priors more closely agree (that is µ_y approaches 2.2), the entropy of the resulting distribution over x increases, so the information obtained by combining them is smaller. For largely different values of the mean of P(y) (e.g. µ_y=−1.0 or µ_y=5.0), the resulting entropy of P ^′(x) is small, and more information was gained by the denotative system from the connotative system. The resulting distributions over x are also shown, demonstrating a clear shift from nurse (P ^′(x)→ 1.0) to doctor (P ^′(x)→ 0.0) as the prior information about the sentiment observed shifts towards the positive (the person demonstrates a behavior with more power). Figure 2(b) shows the denotative entropy and posterior as a function of µ_y, demonstrating the trends with more clarity.

Figure 3(a) shows how the same curves evolve according to a changing value of γ, with a fixed µ_y = 3.0,σ_y = 1.0 (dashed line), P(X = nurse) = 0.7. As Figure 3 shows, when γ is large (>2.0 in this example) there is not as strong an effect between X and Y, and so both follow their prior distributions closely. For small γ, denotative and connotative are more strongly linked, so the sentiment follows the prior over X more closely, becoming more centered around the known mean values of power for the identities of nurse and doctor of 1.9 and 3.0. The denotative posterior is shifted towards X=doctor, as the connotative prior indicates a powerful identity.

The somatic transform naturally shows a trade-off between the uncertainty in X and Y. E.g., Figure 4 shows how the posterior over X and Y changes as a function of P(X = nurse). In this simulation µ_y = 3.5,σ_y = 1.0 and γ = 0.2. As the environment becomes less valid (less predictable or more uncertain, so P(x) is more dispersed or has higher entropy), then P ^′(y) and P ^′(x) will be more heavily influenced by the prior in y: they will make inferences and choose actions that are more in line with connotative (socio-cultural) expectations. In more valid environments, P(x) has lower entropy and dominates the posterior.

Figure 4:

(a) The red line shows a prior state with a less dispersed P(X = nurse) = p with p=0.99, respectively, yielding a posterior for both X and Y that is more in line with the original denotative prior P(x). The blue line (p = 0.5) shows how the posterior is biased towards the prior in y (possibly based on stereotypes). The prior in y is shown as a black dashed line (same for all values of p). S(P) and S(P ^′) denote the prior and posterior entropy of P(X), and P(nurse) and P ^′(nurse) denote the prior and posterior probability of X being nurse. (b) plot of the overall trends in entropy and posterior probability as a function of P(X = nurse).

These basic elements in BayesACT are in line with experiments showing how humans tend to act more pro-socially (cooperate in a public goods game) in ambiguous situations (ones in which risk is hard to evaluate, see Reference Vives and FeldmanHallVives & FeldmanHall (2018)). In this simulation, risk is p = P(X = nurse): if [p, 1 − p] is lower entropy, then risk is more well defined, and so ambiguity (the uncertainty in risk) is lower. It is also in line with experiments showing how the effects of increased ambiguity may result in more political polarization (Reference BailBail et al., 2018). As people are exposed to more heterogeneous discussion online, their political views become more deeply entrenched. More homogeneous discussion leads to more muted political beliefs being expressed. This is explainable by noting that the more heterogeneous discussion leads to greater denotative uncertainty, leading to a more heavy reliance on connotative priors, which may have stereotypes embedded into them. As discussion becomes more homogeneous, increased weight is placed on available evidence, leading to a posterior biased towards a more neutral solution (assuming the evidence is independent of the arguments presented and the stereotypes held).

5.1 Uncertainty and fairness

Reference van den BosVan den Bos (2001) carried out an experiment in which the fairness or unfairness of a situation was evaluated affectively (positive vs. negative) in two conditions: one with induced (primed) feelings of uncertainty enhanced by asking about the emotions felt during uncertain episodes. Two effects are shown. First, the more (perceived) fair condition (where participants got to voice their opinion about a distribution of payoffs, but their opinions were ignored) elicited more positive emotions than the non-fair condition (no chance to voice). Second, the effect was enhanced by the increased uncertain feelings. In BayesACT this can be accounted for by noting that as the emotions associated with uncertainty about the self are evoked, so is the uncertainty in both denotative and connotative identity. However, as uncertainty about denotative identity is increased, the participant (a student) will be more reliant on the connotative system.

Consider a purely denotative solution. In this case, the emotions elicited will not play a role, and a student will think that voicing an opinion may change the payoffs in their favour, and so will prefer that option. However, they don’t know if their voice will be taken into account, so the other option of letting the experimenter decide is only seen as marginally worse. On the other hand, a purely connotative system will focus on the emotional identity only, and so when feelings of uncertainty are evoked (uncertainty is made salient), a more negative emotional identity will react more negatively to the no-voice (default) condition, and the ability to voice opinion will make a more significant difference. This is because the voicing of opinion is an action with emotional meaning that restores feelings of certainty in identity.

We show the simplest possible example, using only non-probabilistic ACT equations in order to motivate the problem.Footnote ¹⁵ We show how BayesACT would modify things at the end of the section. In Reference van den Bosvan den Bos (2001), there are 2× 2 conditions, with half the participants having a “voice” and half not, and half of them having uncertainty made salient, half not. We therefore have two classes of participants: salient and non-salient. The non-salient identities are simply student (EPA:{1.5,0.31,0.75}), with a characteristic emotion of (EPA:{1.5,0.66,0.26}) with closest labels of warm and easygoing. The salient ones we interpret as anxious student (EPA:{−0.2,0.04,1.2}) using the modifier equations of ACT (see Section 2.2), with an emotion of (EPA:{−0.77,−0.30,0.91}) with closest label of envious. These characteristic emotions are those the participants will report in the no-voice condition, so we see that the salient group will have more negative emotions.

In the voice condition, an action is taken by the participant, so we model the student taking the action compromise with, as this is close to the optimal for a student, and is what one would expect the student to do in the fairness test (divide equally). A student who compromises with another student feels emotions of (EPA:{1.9,1.2,0.029}) (closest label patient). On the other hand, if an anxious student is the actor, emotions are more positive (EPA:{2.2,1.3,−0.15}) (closest label remains patient, however).

Figure 5(a) shows these data in a simple plot, where the “E” axis is reversed as in the experiments the participants were asked how “sad” and “disappointed” they were, thus a negative measure.We therefore plot the (inverted) scaled version (to the range 1−7) of the distance between the “E” value of the emotion felt with the mean “E” value of the emotions sad (EPA:{−1.9,−1.7,−2.1}) and disappointed (EPA:{−1.7,1.2,−1.3}). Thus, in the figure, larger y axis values correspond to more negative emotions. Note that these curves correspond in form to that observed in Reference van den Bosvan den Bos (2001), shown in Figure 5(b). In essence, the “fairness” of a behavior is directly a function of how uncertain an agent is.

Figure 5:

(a) ACT simulations of conditions, showing the scaled average of the distance from the emotion felt in the condition with the evaluation of the emotion of sad and disappointed. Scaling to the range 1-7 is done to match scales with that of Reference van den Bosvan den Bos (2001). (b) Results of Reference van den Bosvan den Bos (2001) showing the mean ratings of sadness and disappointment for each of the four cases. In both cases, results are shown as lines for exposition (data is 4 points: the line ends). Larger y axis values correspond to more negative emotions.

The ACT simulations shown in Figure 5 assume a participant is either uncertain (salient case) or not (non-salient case). However, in practice, there will be degrees of uncertainty, possibly based on individual personality (e.g. susceptibility to the probe generating the uncertainty). The simple affect control theory (ACT) model cannot handle this, but BayesACT explicitly trades off between the two cases continuously based on the amount of uncertainty induced. In the case of no uncertainty, the denotative solution takes over. As uncertainty grows, the connotative solution starts to dominate.

Thus, BayesACT can model how agents will be biased towards more connotative solutions by invoked feelings of anxiety leading to feelings of uncertainty. The correspondence between connotative predictions and experimental results of Reference van den Bosvan den Bos (2001) show that people are leaning more heavily on the connotative meanings of the experiment in the uncertainty salient case. As uncertainty in the denotative identity is increased, the posterior over connotative identity becomes more focussed around the connotative meanings (of anxious student). If this were not the case, then the posterior would be more biased towards the denotative reality (of no control over outcomes, so a flat decision function), and the effect would not be as large. One can also see the same effects here as in Reference FeldmanHall and ShenhavFeldmanHall & Shenhav (2019), where uncertainty evoked negative affect, and restorative options for that affective state were preferred to restore affective meanings to something closer to their fundamental values. Lastly, this provides an indication of an experiment to falsify the model, as one could adjust the degree of uncertainty induced and observe the gradual transition across emotional states (essentially interpolating between the end-points in Figure 5).

5.2 Cognitive Dissonance

Cognitive dissonance is a broad term for a large literature of studies on how humans interpret and react to inconsistencies, and includes research on how inconsistency is identified, how affective dissonance is elicited, and how humans resolve inconsistencies (Reference Gawronski, Brannon and Harmon-JonesGawronski & Brannon, 2019). There is growing consensus that the processes of dissonance and dissonance resolution has multiple facets, from the management of purely propositional (logical) inconsistencies (Reference Gawronski, Brannon and Harmon-JonesGawronski & Brannon, 2019), some potentially action-oriented (Reference Harmon-Jones and Harmon-JonesHarmon-Jones & Harmon-Jones, 2018), to the relationship between the self and the situation (Reference Stone and CooperStone & Cooper, 2001). Expected value has recently surfaced as a plausible interpretation that denies consistency its primacy for humans (Reference Kruglanski, Jasko, Milyavsky, Chernikova, Webber, Pierro and di SantoKruglanski et al., 2018). However, there is evidence that “values” are, in fact, exactly on those states that are expected, in the sense that human motivation is to work towards expected states (Reference FristonFriston, 2010), and deviation from expectations over the future create negative affect (Reference Hesp, Smith, Allen, Friston and RamsteadHesp et al., 2021). Thus, expected value and expectations over (denotative) futures may be one and the same, again returning consistency (over future expectations) to the center stage as a prime motivator for human action.

The self-standards model of Reference Stone and CooperStone & Cooper (2001) makes a very similar point to ours about the self being used by humans as a reference mark from which to gauge inconsistent situations. Here we show that BayesACT is able to produce some of the same effects as accounted for by the self-standards model. While we work here on the free/forced choice paradigm, induced compliance and effort justification paradigms could be handled in a very similar way (Reference Harmon-Jones and Harmon-JonesHarmon-Jones & Harmon-Jones, 2018). Induced compliance with incentives (e.g. being forced to write a statement that contradicts moral beliefs, but being rewarded for it) can be modeled as a two-stage game where the positive affective meanings of the reward reduce negative affective feelings from the induced compliance. The belief disconfirmation paradigm, in which evidence is presented that contradicts a belief (Reference Harmon-Jones and Harmon-JonesHarmon-Jones & Harmon-Jones, 2018), is modeled as any transient impression in BayesACT.

BayesACT, as a multi-attribute Bayesian decision network, can in theory also represent any set of propositions, and thus can be used to detect inconsistencies by looking at joint probabilities of related variables, and can compute expected value of outcomes with both consistent and inconsistent beliefs (Reference Kruglanski, Jasko, Milyavsky, Chernikova, Webber, Pierro and di SantoKruglanski et al., 2018). Any such inconsistencies, however, will increase the entropy (dispersion) for the denotative system in BayesACT, and lead to an increasing reliance on connotative interpretations. As a result, denotative action choice distributions are less informative, making behavior initiation more difficult. The induced inconsistencies in the connotative system will be felt as dissonance, often (but not always) as negative emotion. The Bayesian model naturally trades off between the two. As we show in this section, for a simple (and highly stylized) experimental setup, BayesACT shows some of the basic properties of a self-standards type model of cognitive dissonance, combined with those of a propositional inconsistency and expected values model, and may offer a unifying view that combines these different explanations.

Consider a simple demonstrative example in which X corresponds to whether an item is desirable (X = good) or not (X = bad). The corresponding Y (given by y = M(X = x)) is the “E” rating for the item. As demonstrated by Reference Shank and LulhamShank & Lulham, 2017), people are consistent in their ratings of the EPA values of commercial products. For example, iPhones were rated as (EPA:{1.3,1.0,1.5}), whereas Blackberry phones were rated (EPA:{−0.67,−0.71,−0.28}). The study also found that commercial products change people’s identities, and are seen as consistent with some identities and not with others. For example, a CEO with an iPhone is perceived as more powerful as one without. We place a prior on Y that is the same as the identity of the participant.

In Figure 6, the y axis corresponds to the evaluative dimension “E”, and the prior P(y) has µ_y = 2.0 and σ_y = 1.23 (corresponding to the mean and standard deviation of the E rating for child in the University of Georgia 2015 dataset).Footnote ¹⁶

Figure 6:

Simulation of a cognitive dissonance. (a) The posteriors over X and Y shift towards the prior over Y in a forced-choice paradigm, causing a re-interpretation of a bad item as something good. The prior in Y has a stronger effect if it is less dispersed (smaller σ_y, dashed lines). S(P ^′) is the entropy of P ^′(X) and P ^′(bad) is the posterior probability of X = bad. The prior in X is P(X = bad) = 0.8. (b) corresponding plot of the overall trends in entropy and posterior probability as a function of σ_y⁻² (certainty the self is “good”). (c)-(d) same as (a)-(b) but for prior P(X = bad) = 0.5 (free choice paradigm).

We used γ=0.3 and imagine an experiment where the participant is given a Blackberry. The denotative prior is P(X=bad)=0.8, implying the participant believes they have a bad item. After combining the connotative prior (which is essentially saying that any item obtained by the participant must be good, since they are good and expect to have good things), the resulting posterior has a reduced value for P ^′(X=bad) (dropping to 0.34), so is significantly more likely to be on the good side. That is, a participant who originally thought the prize was not as good (P(X=bad)=0.8), has changed her or his mind and now thinks the prize is much better (P ^′(X=bad)=0.34).

Figure 6(a)-(b) also shows the posteriors for a range of smaller (0.5) to larger (2.0) values of σ_y. With a more dispersed prior (larger σ_y), the shift is not as evident (P ^′(X = bad)=0.64), and with a less dispersed prior (smaller σ_y), the shift is even more evident (P ^′(X = bad)=0.00024). BayesACT predicts that agents will deal with less valid environments by leaning more heavily on their connotative system. Thus, the resulting P ^′(x) is low precisely because the connotative system has “taken over” and it has become more imperative to justify receiving the lesser gift.

Any actual experiment would need to take a range of “types” of σ_y into account by measuring the distribution over σ_y in the population and then integrating them out as:

(7)

where P(σ_y = j) is the empirical prior for the population under study.

Figure 6(c)-(d) shows the same simulation but this time with P(X = bad) = 0.5. With this prior, either item is equivalent from an expected utility standpoint, and so an optimal denotative strategy is to choose randomly, thus mirroring the free choice paradigm (Reference BrehmBrehm, 1956) in which two equally desirable items are to be chosen between. The results are very similar here, with the obtained (chosen) item being evaluated much more positively (even more so than in the forced choice case considered above).

In the self-standards model (Reference Stone and CooperStone & Cooper, 2001), a focus on either personal attributes of the self, or societal norms can both create dissonance, as can non-self related inconsistencies. In the BayesACT view, societal norms are implicitly embedded in the self-sentiment, and so the first two aspects are really considered to be the same when viewed through the connotative lens of affect control theory. Logical inconsistencies (Reference Gawronski, Brannon and Harmon-JonesGawronski & Brannon, 2019) can also be accounted for in BayesACT, although we have not explored this in detail here. However, changes in expected value certainly can, but we argue that affective reactions to changes in expected (denotative) value are tempered by affective reactions to changes in (connotative) meanings about the self. Thus, a student who expects to do badly on a test is confronted with inconsistency if he does well, but this is argued by Reference Kruglanski, Jasko, Milyavsky, Chernikova, Webber, Pierro and di SantoKruglanski et al., 2018) not to create negative affect as predicted by classical dissonance theory. However, as pointed out by Reference Harmon-Jones and Harmon-JonesHarmon-Jones & Harmon-Jones (2018), other elements (such as self-concept changes) will also play a role, possibly overriding the negative affective reactions to inconsistency. In BayesACT, these effects are handled as changes in denotative state (from doing badly on the test, to doing well), increase in denotative entropy as a result, and thereby increased salience of connotative meanings (shifting from “bad student” to “good student”). Similarly, denotative inconsistencies that have weak connotative meanings (e.g. drawing colored balls from a box (Reference Kruglanski, Jasko, Milyavsky, Chernikova, Webber, Pierro and di SantoKruglanski et al., 2018)) would not change the posterior distribution over the connotative state, and so would not generate any non-characteristic affect, as observed in empirical results (Reference Kruglanski, Jasko, Milyavsky, Chernikova, Webber, Pierro and di SantoKruglanski et al., 2018).

As a unifying view, BayesACT shows that the negative affect is less related to inconsistency or value per se, but rather to the effects that this has on the connotative state, modulated by uncertainty. For example, BayesACT would predict someone with a strong negative self-concept (who thinks of themselves as a “bad student”), will discount the positive test score instead, possibly arriving at a denotative interpretation that they did badly in any case (regardless of the evidence to the contrary). This means cognitive dissonance experiments that explicitly queried participants for their identity would yield falsifiable BayesACT predictions such as this. Many of the disagreements in cognitive dissonance theories could be resolved by considering that there are two types of inconsistency which are tightly related: dissonant cognitions (or logical inconsistencies), and dissonant feelings (invalidation of self-concepts). This mirrors Festinger’s original proposal of two determinants of dissonance: cognition and importance to the individual (Reference FestingerFestinger, 1962). Dissonant cognitions (or incoherence between denotative priors and evidence in BayesACT) do not elicit affect directly in BayesACT, but they increase entropy leading to increased reliance on connotative meanings, which are the source of affective reactions.

One key element of the BayesACT simulations described above is that the certainty in the self-identity is highly relevant for the amount of dissonance caused. In the cognitive dissonance experiment described, the variance of the self-identity is coupled with the act of “owning” something. In the slightly broader category of cognitive biases normally labeled as self-affirmation (Reference Sherman and CohenSherman & Cohen, 2006), similar styles of experiments have shown how people will be more objective in the analysis of facts when self-affirmed. To put this in the same language as the cognitive dissonance experiments, they are more willing to re-interpret facts that disagree with their values in a way that changes their view on those facts. The increased dispersion in the denotative posterior allows an agent to entertain scenarios that disagree with their values.

Confirmation biases are another form of the same effect. This is the observation that people’s prime concern is what others think of them, and that this drives them to seek evidence that agrees with their beliefs. In BayesACT, this concern is modeled in the connotative state, and reasoning is used to construct a viable denotative trajectory that leads to the connotative prescription. That is the difference between should and would (Reference PattersonPatterson, 2014; Reference Martin and LemboMartin & Lembo, 2020), or between must I (reason) and can I (intuition) (Reference HaidtHaidt, 2012).

5.3 Probabilistic Constraint Networks in BayesACT

In this section, we briefly sketch how to map a connectionist parallel constraint satisfaction (PCS) model to a BayesACT model. Our goal is to outline how the two types of model are largely compatible. The primary difference between them is in the learning bias they apply, and so the selection of one over the other would come down to a much more detailed analysis of which bias is more successful in generalizing across situations, an empirical question yet to be answered.

We base this analysis on a recent experiment by Reference Simon, Stenstrom and ReadSimon et al., 2015) where a participant is asked to judge a student named “Debbie” who is accused of cheating, based on a number of facts that are manipulated to make experimental conditions. The participants are assigned the role of Judicial Officer in charge of deciding on whether to suspend the student or not. A key element in such a PCS model is a pair of inhibitory nodes that model complementary concepts, such as whether Debbie is guilty or not. In BayesACT, each such pair is described by a single random variable with two states (e.g. a binary variable called “guilty” in the set X with values “true” and “false”). The probability distribution over these two states maps to the “activation” of the pair of nodes in the PCS. For example, suppose the activation of the “not guilty” and “guilty” nodes in the PCS are 0.72 and 0.45. This could map to a probability distribution P(guilty) ∝ [e ^0.72,e ^0.45]∝[0.58,0.43] over the “guilty” random variable in BayesACT. Each pair of guilt and innocence facts are modeled with binary observation variables in BayesACT, and each has a higher probability given its corresponding value of the state. That is, P(guilt fact|guilty) > P(guilt fact|innocent) and P(innocent fact|innocent) > P(innocent fact|guilty). The emotional nodes such as “sympathy” would be modeled as identity traits in BayesACT, such as sympathetic judicial officer, and in the somatic transform linking positive valence and “liking” with the identities assumed in the interaction (e.g. the participant might “like” Debbie because they have a friend named Debbie). Motivation leading to action in the PCS is modeled with a preference or utility function that ranks outcomes in BayesACT. In contrast to the model by Reference Simon, Stenstrom and ReadSimon et al. (2015), the described mappings are not designed specifically by the researcher, but taken from empirical EPA databases that reflect culturally shared connotative meaning structures (Reference Ambrasat, von Scheve, Conrad, Schauenburg and SchröderAmbrasat et al., 2014; Reference HeiseHeise, 2010).

Decision theoretically, the BayesACT POMDP will select the “correct” action (convict the guilty and acquit the innocent), reducing the problem to one of inference about the guilty/innocent denotative state variable. Nevertheless, BayesACT explicitly includes a variable representing action that is deeply connected to its affective meaning through the somatic transform. Further, the identities selected for the two persons being modeled will be based upon the text they read, and would thus provide a fast estimate of a probability distribution over the affective space indicating how the best behavior should “feel”. This distribution then weights the denotative action distribution, increasing the likelihood of the agent taking the action that is affectively more aligned with this prediction.

To get a better feel for the identity dynamics involved, suppose we choose the identities of juror (EPA:{0.66,1.3,0.060}) Footnote ¹⁷ and student (EPA:{1.5,0.31,0.75}). The identity of the student is fluid, however, because it depends (through the somatic transform) on the denotative state variable of guilt/innocence. That is, we will have a prior belief that students will be more likely to be innocent than guilty, rooted in culturally shared connotations of the concept student. We also consider two other identities for Debbie: friend (EPA:{2.8,1.9,1.4}) and delinquent (EPA:{−1.8,−0.78,0.41}). Considering the deflections (emotional incoherence) of an ACT simulation of this situation, we use behaviors of convict (EPA:{0.05,1.36,0.34}) and forgive (EPA:{2.6, 2.0, 0.40}).Footnote ¹⁸ Further, we adjust the juror identity to sympathetic juror using modifier equations to model the condition in which the sympathy is induced, giving a rating of sympathetic juror of (EPA:{1.3,1.1,−0.34}).

Considering the first two columns in Table 1, the deflection caused by forgiving is lower than convicting in the sympathetic juror case, while it is higher in the non-sympathetic juror case. On average therefore, in agreement with the results of Reference Simon, Stenstrom and ReadSimon et al. (2015), there will be more acquittals in the sympathy case because of this effect. Should the juror consider the student to be a delinquent, on the other hand, then the more likely behaviour will be to convict, regardless of sympathy. Finally, forgiveness is more likely if Debbie is considered a friend. Although three pairs of identities does not give conclusive evidence, it is certainly evidence that the BayesACT model would show the same effects when taken in population averages. Participants may not all assign identities of student or delinquent to Debbie, and may not all assign identities of juror to themselves. However, we know that, on average, people will consider cheaters to be more negative and powerless identities, and so the same effect will show up and would be averaged over in BayesACT.

Table 1:Deflections for different conditions where the juror or friend (actor) can be sympathetic or not and the object (client) can be a student, delinquent or friend. The lowest deflection for each actor-object pair is shown in bold.

As stated earlier, this example gives a simple mechanism for falsifying BayesACT, as BayesACT predicts that if we change the participant’s assumed role (identity), the final decisions would change. The model of Reference Simon, Stenstrom and ReadSimon et al. (2015) would make the same prediction unless all the weights were modified to reflect this or a new node was added to the coherence network. Table 1 (last two columns) further shows what the deflections look like if the situation was re-framed and the participants were told to imagine they were a friend of Debbie’s. In this case, the deflections are generally higher for convicting, because a friend is inherently relational and somewhat expects the object-person to be a friend as well, so dealing (as friend) with a student or delinquent is more deflecting (less likely). Further, the best action to take is always to forgive if the object is a student or a friend, regardless of sympathy.

While a new node for the identity could be added to the Simon et al. model, it would need to be precisely tailored for the domain, and connections added with weights that would determine that friends don’t convict students, for example. BayesACT is more general because one needs only to change the identity, and the same model can be used. Further, uncertainty in BayesACT allows one to modify the experimental condition making it more or less ambiguous, and this can be explicitly taken into account. BayesACT predicts that making the facts less ambiguous would reduce the effect of the connotative network and thus of the identity labels.