Information Technology Reference
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9 The Information Flow Connection
In this section, we shall define the information flow connection between the
classifications of budgets and project plans. As we consider budgets to precede
project plans in a flow of information, we require that changes done in a budget
are likewise reflected in a succeeding project plan.
Consider a budget and a project plan which satisfy the criteria of the charac-
terization connection . Changing the budget through specialization (see Sect. 4.2)
should imply that the corresponding project plan needs to be specialized likewise.
The reason is that when specializing the budget we are decreasing its financial
scope, meaning that the set of project plans executable within its restrictions,
cannot increase. Hence, the project plan of concern should be specialized in such
a way that it is still executable within the specialized version of the budget.
The implication is, however, not a bi-implication as specializing the project plan
does not put restrictions on the preceding budget. However, if the project plan
is generalized, it implies that the budget must be generalized likewise. Again,
this is not required in the other direction.
The above states that order must be preserved when specializing and gen-
eralizing budgets or project plans. This is a property of the definitions of the
partial orders and of the Galois predicate. We shall say that the connection is
order-preserving . If the above implication is satisfied, we shall say that we have
an information flow connection between the concepts. If this is not the case, it
is worth investigating the model as we may then have inconsistency in the way
specialization/generalization works together with the characteristics connection ;
hence, inconsistency in the understanding and the model of the concept relation.
Theorem 3. The information flow connection between budgets and project plans
with respect to the Galois predicate, is order-preserving:
axiom
b 1 ,b 2 :B,pp 1 ,pp 2 :PP
b 2
b 1
φ (b 1 ,pp 1 )
φ (b 2 ,pp 2 )
pp 2
pp 1
Proof. We can specialize a budget in two ways: (i) by reducing costs, and (ii) by
breaking down costs figures. We shall consider these cases separately.
Reducing costs:
Reducing a cost means subtracting this cost from the cost of the budget figure.
From the definition of φ , we have:
sumcost(rel_map(pp,bf,wrkidx),prcidx)
cost(b(bf))
c
sumcost(rel_map(pp,bf,wrkidx),prcidx) + c
cost(b(bf))
Let rm 2 = sumcost(rel_map(pp 2 ,bf,wrkidx),prcidx) + c
and let rm 1 = sumcost(rel_map(pp 1 ,bf,wrkidx),prcidx) . As we cannot have neg-
ative costs, the only way of satisfying the above is for pp 2 to designate less re-
sources than pp 1 . That is, pp 2 must be a sub-graph of pp 1 and the individual
 
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