the more credible the belief. $\Box$

A reasonable semantics should respect the power of majority; indeed, $F$ is true (false) in $S$ if it is true (false) in all models of $F$. Obeying such an unanimity, would it be reasonable to disregard a majority of 99.9% or even 80%?

As PMM suggests a belief regarding the truth value of $F$, we may say that the set of models of $S$ offers an *evidence* of $F$, $E(S, F)$. We would like the evidence to provide a quantitative measure of credibility of the corresponding belief. To normalize the value of evidence for all $S$ and $F$ such that $0 \le E(S, F) \le 1$, it is reasonable to require that $E(S, F) = 1$ for $S \models F$, $E(S, F) = 0$ for $S \models \neg F$, and $E(S, F) + E(S, \neg F) = 1$ for all $S, F$. More requirements are presented in @loz94 leading to the following definition.

\[def-evid\] *Evidence* of $F$ in $S$: $$E(S, F) = \frac{|MOD(S \cup \{F\})|}{|MOD(S)|}. \; \; \; \Box$$

PMM suggests that $F$ is true if $E(S, F) > 0.5$ or $E(S, F) = 0.5$ (the latter is chosen to avoid ambiguity; see also 