formula $F$ is true in the present state of the world is $$p(F) = \sum_{\mu \in MOD(S \cup \{F\})} p(\mu)$$ where $MOD(S \cup \{F\}) = \{\mu | \mu \in MOD(S) \wedge \mu \models
F\}$ is the set of models of $S$ implying $F$.

If $p(F) > 0.5$ then it is reasonable to believe that $F$ is more likely to be true than false in the present state of the world, and the larger $p(F)$, the more credible this belief.

The problem, however, is that in most practical cases there is no reliable information regarding the distribution of $p(w)$. In the absence of this information let us assume just for the moment that all possible worlds are equiprobable, and sets $W$ and $MOD(S)$ are finite. Appendix B shows a way to relax these limitations in case that certain knowledge is available about probability of possible worlds and structure of a given system and its domain.

The assumptions of the previous paragraph lead to the following approach.

\[def-PMM\] Believe that a formula $F$ is more likely to be true than false in a state of the world if $F$ is true in a majority of models of $S$. The larger the majority, 