But in the absence of a sufficient statistics regarding $p(w)$ one has to rely on $E(S, a)$ and believe that any typical atom is not less likely to be true than false in the present state of the world. On the other hand, the need to avoid inconsistency may force a non-oblivious reasoner to adopt beliefs in negation of some typical atoms. So questions arising in any reasoning system intended for answering multiple queries are:

> Given a set of queries $\{F_1, \ldots , F_k\}$, is there a state of the world in which beliefs in the truth of typical values $\{\widehat{F}_1, \ldots , \widehat{F}_k\}$ hold for all $1 \le i \le k$, i.e. is there a model $m$ of $S$ such that $m \models \bigwedge^k_{i=1} \widehat{F}_i$? What is the value of evidence $E(S, \bigwedge^k_{i=1} \widehat{F}_i)$?

The answer to the first question is positive if the latter evidence is larger than zero.

Let $A^{(k)}$ be a set of $k$ literals $l$ such that $l \in \{a, \neg a\}$, $a \in Base(S)$, and $A^{(k)}_{\wedge} = \bigwedge_{l \in A^{(k)}} l$. The following theorem estimates the value of evidence of $A^{(k)}_{\wedge}$.

\[th-evid\] $\max(0, \alpha, \beta) \le E(S, A^{(k)}_{\wedge}) \le \min(1,
\gamma)$, where\
$$\begin{aligned}
