truth of $F$ in the present state of the world?

In order to answer various multiple queries consistently a reasoner has to choose one particular model $\mu$ of $S$ (a *preferred model*) and then believe that $F$ is true in the reality iff $\mu \models F$. If $S \models F$ or $S
\models \neg F$ then the choice of $\mu$ does not matter; however, if $F$ is incomplete in $S$ then $F$ is true in some models, but false in the others. Which is the correct value of $F$ in the present state of the world? With any choice of $\mu$ there is a non-zero probability that the belief in $F$ implied by $\mu$ is false in the present state of the world. So reasoning with incomplete information is *prone to errors*.

The way of choosing the preferred model provides a semantics for the process of reasoning. Whatever this way is, errors are inevitable since the preferred model may not fully conform to the present state of the world. The smaller the expected number (or the severity) of errors, the more reliable the semantics. Numerous approaches to reasoning with incomplete information have been developed including *Nonmonotonic Logics* [@ant97; @bre07; @sho87] 