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.

Definition 2.1 (Principle of majority of models, 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, the more credible**
the belief. ✷
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** ≤ E(S, F) ≤ 1, it is reasonable to require that E(S, F) = 1 for S |= F, E(S, F) =
0 for S |= ¬F, and E(S, F) + E(S,¬F) = 1 for all S, F**. More requirements are**
presented in Lozinskii (1994) leading to the following definition.

Definition 2.2 **Evidence** of F in S:

$$E(S,F)={\frac{|M O D(S\cup\{F\})|}{|M O D(S)|}}.\quad\Box$$

$$\mathrm{(2)}$$
|MOD(S)|. ✷ (2)
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 footnote 3). Given a query regarding the truth value of F**, a reasoner may not only return 'true' or 'false', but also** attach the value of E(S, F**) to the answer to give a measure of credibility of the** latter. In cases where accepting an erroneous answer can have very undesirable consequences, a query can require a certain level of credibility, for example, ignoring answers with evidence less than 0.9.

## 3 Oblivious Vs. Non-Oblivious Reasoning

In the absence of sufficient statistical information the evidence E(S, F) is regarded as an approximation of the probability p(F) that F **is true in a randomly**
chosen possible world, that is the probability that the belief in the truth of F is correct in the present state of W.