Relating Domain Concepts Intensionally by Ordering Connections - Formal Methods and Hybrid Real-Time Systems - page 215

objects of two concepts. The connection adds intensional knowledge as it de-
scribes what effect it has on objects of one kind to change objects of another.
We have defined the steps of the method and expressed the axioms of the two
connections.
In order to put the method to work, we have formally modelled the notions
of budgets and project plans. In addition, we have modelled the necessary medi-
ating ties which (as prescribed by the method) are the additional concepts that
are necessary in order to establish a formal relation between the two concepts
in question.
Furthermore, the two ordering connections have been defined for the models.
The characteristics connection between budgets and project plans, has been
defined such that project plans relate to budgets if and only if they are executable
within the financial restrictions of the budgets; and budgets relate to project
plans if and only if they (at least) designate the necessary expenses for executing
the project plans. We have shown that the connection is a Galois connection. The
information flow connection between budgets and project plans, has been defined
such that specialization of budgets cannot imply generalization (and vice versa)
of succeeding project plans if the characteristics connection is to be maintained.
Thereby, we have ensured that the concept relation between budgets and project
plans maintains the systematics of concretising information from budgeting to
project planning.
The axiom of the information flow connection — utilizing the characteristics
connection — shows that we are able to reason (to some extend) about the ra-
tionality of how the domain concepts have been modelled. Isolated, neither of
the two connection incorporate domain knowledge but are mathematical axioms
over domain models. This means that the predicate founding the Galois con-
nection might define other criteria for objects to relate. Similar considerations
may apply for the classification of objects. By putting the two connections to-
gether, however, we provide the kind of domain reason abilities that are often
missed when following an informal modelling approach. Future work is to focus
on strengthening the formal foundation on this area.
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