Emotion Regulation

Identification Stage

• At the perception component, Agent \(m\) Perceives Agent \(n\)’s Emotion \(e\).
• At the valuation component, Agent \(m\) Valuates Emotion \(e\) against Goals \(g\) (all are Currently Active and at least one is an Emotion Goal) in light of Factors \(f\) (all are Relevant to the Valuation).
• At the action component, Agent \(m\) Acts on Action \(a\) which triggers the Selection Stage if and only if the Valuation exceeds threshold \(\text{T}(m)\).

\[ \forall m \forall n \ (\underbrace{\text{IS}(m,n)}_{\text{Identification Stage}} \rightarrow \] \[ \exists e \exists g \exists f \ ( \] \[ \underbrace{\text{P}_{\text{IS}}(m,e) \land \text{B}_{\text{IS}}(e,n)}_{\text{Perception}} \text{ } \land \] \[ \underbrace{\text{V}_{\text{IS}}(m,e,g,f) \land (\forall x (x \in g \rightarrow \text{CA}_{\text{IS}}(x))) \land (\exists y (y \in g \land \text{EG}_{\text{IS}}(y))) \land (\forall z (z \in f \leftrightarrow \text{RV}_{\text{IS}}(z,m,e,g)))}_{\text{Valuation}} \text{ } \land \] \[ \underbrace{(|\text{V}_{\text{IS}}(m,e,g,f)| > \text{T}_{\text{IS}}(m)) \leftrightarrow (\exists a \text{ } \text{A}_{\text{IS}}(m,a) \land \text{SS}(m,n))}_{\text{Action}} \] \[ )) \]

Selection Stage

Let \(m\) be a variable for an element of \(ER\), where \(ER\) is the set of emotion regulating agents. Let \(n\) be a variable for an element of \(EG\), where \(EG\) is the set of emotion generating agents. Let \(s\) be a variable for an element of \(\mathcal{P}(S_m)\), where \(S_{m}\) is the set of emotion regulation strategies for \(m\). Let \(g\) be a variable for an element of \(\mathcal{P}(G_m)\), where \(G_{m}\) is the set of goals for \(m\). Let \(f\) be a variable for an element of \(\mathcal{P}(F_m)\), where \(F_{m}\) is the set of contextual factors for \(m\). Let \(a\) be a variable for an element of \(A_{m}\), where \(A_{m}\) is the set of possible actions for \(m\). Let \(n_{\text{SS}}\) be an element of \(\mathbb{R}\) above which \(|s|\) is considered to be sufficiently large.

Let \(\text{SS}\) be a two-place predicate for an \(m\) that is at the selection stage of emotion regulation for an \(n\). Let \(\text{P}_{\text{SS}}\) be a two-place predicate for an \(m\) that perceives \(s\). Let \(\text{V}_{\text{SS}}\) be a four-place predicate for the evaluation by \(m\) of \(r \in s\) against \(g\) in light of \(f\). Let \(\text{CA}_{\text{SS}}\) be a one-place predicate for an \(x \in g\) that is currently active. Let \(\text{EG}_{\text{SS}}\) be a one-place predicate for a \(y \in g\) that is an emotion goal. Let \(\text{RV}_{\text{SS}}\) be a four-place predicate for a \(z \in f\) that is relevant for the evaluation by \(m\) of \(r \in s\) against \(g\) in light of \(z\) at the selection stage. Let \(\text{A}_{\text{SS}}\) be a two-place predicate for an \(m\) that acts on \(a\). Let \(\text{MS}\) be a three-place predicate for an \(m\) that is at the implementation stage of emotion regulation for an \(n\) using emotion regulation strategies \(r \in s\).

At the perception component, \(m\) perceives a sufficiently large number of \(s\). At the valuation component, \(m\) evaluates each emotion regulation strategy in \(s\) against \(g\) (all are currently active, and at least one is an emotion goal) in light of \(f\) (all are relevant). At the action component, \(m\) acts on \(a\), and the action triggers the implementation stage of emotion regulation for \(m\) for \(n\) using emotion regulation strategies \(r \in s\).

\[ \forall m \forall n \ (\underbrace{\text{SS}(m,n)}_{\text{Selection Stage}} \rightarrow \] \[ \exists s \exists g \exists f \ ( \] \[ \underbrace{\text{P}_{\text{SS}}(m,s) \land (|s|\geq n_{\text{SS}})}_{\text{Perception}} \text{ } \land \] \[ \forall r \in s \text{ }( \] \[ \underbrace{\text{V}_{\text{SS}}(m,r,g,f) \land (\forall x (x \in g \rightarrow \text{CA}_{\text{SS}}(x))) \land (\exists y (y \in g \land \text{EG}_{\text{SS}}(y))) \land (\forall z (z \in f \leftrightarrow \text{RV}_{\text{SS}}(z,m,r,g)))}_{\text{Valuation}} \text{ } \land \] \[ \underbrace{(\forall t \in s \text{ }(|\text{V}_{\text{SS}}(m,r,g,f)| \geq |\text{V}_{\text{SS}}(m,t,g,f)|) \leftrightarrow (\exists a \text{ } \text{A}_{\text{SS}}(m,a) \land \text{MS}(m,n,r)))}_{\text{Action}} \] \[ ))) \]

Implementation Stage

Let \(m\) be a variable for an element of \(ER\), where \(ER\) is the set of emotion regulating agents. Let \(n\) be a variable for an element of \(EG\), where \(EG\) is the set of emotion generating agents. Let \(s\) be a variable for an element of \(\mathcal{P}(S_m)\), where \(S_{m}\) is the set of emotion regulation strategies for \(m\). Let \(g\) be a variable for an element of \(\mathcal{P}(G_m)\), where \(G_{m}\) is the set of goals for \(m\). Let \(f\) be a variable for an element of \(\mathcal{P}(F_m)\), where \(F_{m}\) is the set of contextual factors for \(m\). Let \(a\) be a variable for an element of \(A_{m}\), where \(A_{m}\) is the set of possible actions for \(m\). Let \(n_{\text{SS}}\) be an element of \(\mathbb{R}\) above which \(|s|\) is considered to be sufficiently large.

Let \(\text{SS}\) be a two-place predicate for an \(m\) that is at the selection stage of emotion regulation for an \(n\). Let \(\text{P}_{\text{SS}}\) be a two-place predicate for an \(m\) that perceives \(s\). Let \(\text{V}_{\text{SS}}\) be a four-place predicate for the evaluation by \(m\) of \(r \in s\) against \(g\) in light of \(f\). Let \(\text{CA}_{\text{SS}}\) be a one-place predicate for an \(x \in g\) that is currently active. Let \(\text{EG}_{\text{SS}}\) be a one-place predicate for a \(y \in g\) that is an emotion goal. Let \(\text{RV}_{\text{SS}}\) be a four-place predicate for a \(z \in f\) that is relevant for the evaluation by \(m\) of \(r \in s\) against \(g\) in light of \(z\) at the selection stage. Let \(\text{A}_{\text{SS}}\) be a two-place predicate for an \(m\) that acts on \(a\). Let \(\text{MS}\) be a three-place predicate for an \(m\) that is at the implementation stage of emotion regulation for an \(n\) using emotion regulation strategies \(r \in s\).

At the perception component, \(m\) perceives a sufficiently large number of \(s\). At the valuation component, \(m\) evaluates each emotion regulation strategy in \(s\) against \(g\) (all are currently active, and at least one is an emotion goal) in light of \(f\) (all are relevant). At the action component, \(m\) acts on \(a\), and the action triggers the implementation stage of emotion regulation for \(m\) for \(n\) using emotion regulation strategies \(r \in s\).

\[ \forall m \forall n \ (\underbrace{\text{MS}(m,n)}_{\text{Implementation Stage}} \rightarrow \] \[ \exists t \exists g \exists f \ ( \] \[ \underbrace{\text{P}_{\text{MS}}(m,t) \land (|t|\geq n_{\text{MS}})}_{\text{Perception}} \text{ } \land \] \[ \forall c \in t \text{ }( \] \[ \underbrace{\text{V}_{\text{MS}}(m,t,g,f) \land (\forall x (x \in g \rightarrow \text{CA}_{\text{MS}}(x))) \land (\exists y (y \in g \land \text{EG}_{\text{MS}}(y))) \land (\forall z (z \in f \leftrightarrow \text{RV}_{\text{MS}}(z,m,c,g)))}_{\text{Valuation}} \text{ } \land \] \[ \underbrace{(\forall d \in s \text{ }(|\text{V}_{\text{MS}}(m,c,g,f)| \geq |\text{V}_{\text{MS}}(m,d,g,f)|) \leftrightarrow (\exists a \text{ } \text{A}_{\text{MS}}(m,a) \land \text{IM}(m,n,c)))}_{\text{Action}} \] \[ ))) \]

Note: \(\text{RV}_{\text{⋅}}(\alpha,\beta,\gamma,\delta)\) if and only if \(|\text{V}_{\text{⋅}}(\beta,\gamma,\delta,\alpha)| \neq |\text{V}_{\text{⋅}}(\beta,\gamma,\delta)|\).