beliefs.

Typical atoms
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$S$ is supposed to be formulated in a first order language, so using the terminology of Predicate Calculus let the *base* of $S$ be a set of all ground instances of all atomic formulas corresponding to all predicates occurring in $S$: $$Base(S) = \{P^{(k)}(t_1, \ldots , t_k)\},$$ such that $P^{(k)}(x_1, \ldots , x_k)$ occurs in $S$, $D_i$ is the *domain* of $x_i$, and $t_i \in D_i$\
for $1 \le i \le k$.

For each ground atomic formula $\mathbf{a} \in Base(S)$ let $\mathbf{\hat{a}}$ denote the *typical atom* corresponding to $\mathbf{a}$ such that the evidence of $\mathbf{\hat{a}}$ is at least as large as that of $\mathbf{\neg \hat{a}}$. So[^2] $$\mathbf{\hat{a}} = \left\{ \begin{array}{r l}
\mathbf{a} & if \; E(S, \mathbf{a}) \ge 0.5 \\
\neg \mathbf{a} & otherwise
\end{array} \right.$$ For a formula $F$ we define its *typical value* $\widehat{F}$ by substituting $F$ for $\mathbf{a}$ in expression (5).

Evidence $E(S, a)$ is introduced in order to be used as an approximation of $p(a)$. The larger the difference $|E(S, a) - 0.5|$, the better this approximation. However, if $E(S, a)$ is close to $0.5$, it may diverge from $p(a)$ even qualitatively such as $E(S, a) > 0.5$ but $p(a) < 0.5$. 