Relating Domain Concepts Intensionally by Ordering Connections - Formal Methods and Hybrid Real-Time Systems - page 214

resource usage of nodes in pp 2 cannot be larger than the individual resource us-
age of corresponding nodes in pp 1 . That is, pp 2 ≤ pp 1 .

Breaking down cost figure:
This means that we compare a sub-budget b 2 x in the specialized budget b 2 with
a corresponding sub-budget which is

B is by
definition the largest cost. This means that for each budget figure bf 2 x in b 2 x ,we
have: cost(b 2 x (bf 2 x ))

B in the budget b 1 . The cost of

≤ B . This corresponds to a cost reduction of each figure
bf 2 x . Hence, the axiom holds; given the result of the above case. The cases of
generalization budgets, are dual to the above.

10 Relating the Two Connections

Even though the characteristics connection is monotonously decreasing and the
information flow connection is order-preserving, the two connections are inti-
mately connected. We shall argue this by taking origin in the characteristics
connection and show that this leads to the information flow connection .
Consider a set of budgets and a set of project plans. Assume that each project
plan is executable within the restrictions of each budget in the set. Thereby, it is
also executable within the restrictions of meet applied pair-wise on the budgets
in the set. This can easily be seen as follows. For budgets having distinct budget
figures satisfying all, is impossible. For budgets with overlapping budget figures,
satisfying these budgets means that the project plan should comply with only the
common budget figures; else it does not satisfy every budget. Hence, satisfying
all the budgets in the set, corresponds to satisfying meet applied pair-wise on the
budgets in the set. Budget meet is a specialization of both argument budgets;
in the above example, a specialization of each budget in the set.
According to the characteristics connection , extending the set of budgets can-
not extend the corresponding set of executable project plans. Hence, the special-
ization due to applying meet , cannot extend the corresponding set of executable
project plans. That is, meet applied pair-wise on a set of budgets is only satisfied
by a project plan which is a specialization of every project plan in the set. We can
see specialization of budgets as combining budgets and apply meet . Hence, spe-
cializing a budget means specialization of a corresponding project plan. Thereby,
we got from the characteristics connection to the information flow connection .

11 Conclusion

In this paper, we have proposed a modelling method for relating domain concepts
intensionally. The method suggests that domain concepts (formally modelled)
are related by two ordering connections. The former connection is called the
characteristics connection and is a Galois connection between objects of one
concept and objects of another concept. The connection adds intensional know-
ledge as it states how objects of one concept are part of the characteristics of
objects of another concept. The latter connection is called the information flow
connection and is an order-preserving connection between classifications of the