In this page we translate the information in Figure 2.6 into a more conventional logical notation, ready for further refinement. As in the translation of our operator diagram, the algorithm looks complex but can be automated. Our method for this is as follows:
. Construct an expression: 
where
each 
is a new variable restricted to type 
.
For example the top-level expression in Figure 2.6 is: 
.
on which it
depends (found by following backwards along the arrows on the diagram to its
data sources) and the type 
of its result. Now construct a term
where
each 
is either a variable 
, if 
is the same type as
, or, if not, is a new variable. Any new variables are
existentially quantified. For example the 
function on
Figure 2.6 yields the expression:
.
, the left side of which comes from the first step and
where C is the conjunction of all the terms from the
previous step. For our example, this gives us
expression 1 shown below.
on which it depends (by following backwards
along the arrows on the diagram to its data sources). Find the set of
data types 
which the function produces (by
following the arrows leading out of its oval). Construct an
expression 
where each 
is a new variable restricted to type 
.
All the variables 
are existentially quantified.
For example the 
function oval in Figure 2.6
yields expression 2 shown below.
We have a risk assessment for a person and some data source if there is some model which we can select for that person and data, and we can assess the loan risk based on that model.
For every person and data store we can select some model.
