**3. Shafer's Theory of Evidence**

The mathematical theory of evidence was defined by Glen Shafer in the 1970s to generalize the probability theory [9]. In particular, if probability functions are considered, they obey the additivity rule, so that the following holds:

$$\operatorname{Pro}(\mathcal{U}) + \operatorname{Pro}(\overline{\mathcal{U}}) = 1 \tag{1}$$

where *U* and *U* are complementary sets.

However, in Shafer's (and also the authors') opinion, the additivity rule is not able to handle correctly all possible situations of knowledge/unknowledge. Therefore, he generalizes this rule, and to do this, he defines the belief functions *Bel*, for which the superadditivity rule applies:

$$Bel(\mathcal{U}) + Bel(\overline{\mathcal{U}}) \le 1 \tag{2}$$

Given a certain statement *A*, the degree of belief *Bel*(*A*) is a judgment. This means that, given *A*, different individuals with different levels of expertise regarding *A* might provide different judgments. In his book, Shafer writes explicitly:

"*Whenever I write of the 'degree of belief' that an individual accords to the proposition, I picture in my mind an act of judgment. I do not pretend that there exists an objective relation between given evidence and a given proposition that determines a precise numerical degree of support. Rather, I merely suppose that an individual can make a judgment* ... *he can announce a number that represents the degree to which he judges that evidence supports a given proposition and, hence, the degree of belief he wishes to accord the proposition*" [9]

In his book, Shafer also provides two examples to show that belief functions are more suitable to handle knowledge/unknowledge with respect to probability functions: the example of the Ming vase and the example of Sirius star are here briefly recalled.
