Propositional probabilities are probabilities assigned to particular propositions or assertions.
It is not a priori clear how to assign probabilities to logical
formulas in a consistent and useful manner. It can be done as sketched below
in [512] , following [106] .
The result is simply that we
denote the probability of a formula 
We
also find it convenient to denote certainty as follows.
Where propositional probabilities are probabilities assigned to particular propositions or assertions, statements of statistical probability make assertions about the proportion of individuals from a particular set that are members of some other set; e.g. the proportion of individuals having a fitness equal or higher than average from the real population (out of all possible populations). We may also view this as attributing a property to a proportion of individuals in a set with a certain probability.
The major difference compared with propositional probabilities is that the statistical probability operator must specify a set of placeholder variables - we are not talking about a particular individual, but about a set of individuals.
We may define the statistical probability formally as follows; for details see [106] .
We also need a measuring function, known in statistics and probability
theory as a random variable (see any standard reference on probabilities).
These are used to map individual objects (or properties of objects) to real
numbers in order to discuss these objects or properties. In the genetic
algorithm the most important function is that of fitness, 
,
where 
is an individual in the population.