Relating Domain Concepts Intensionally by Ordering Connections - Formal Methods and Hybrid Real-Time Systems - page 195

Define a Galois predicate. Quantifying over objects of the formalized do-
main concepts, we explicitly formalize the predicate stating the criteria that
objects of the concepts must satisfy in order to relate to each other.
We call this predicate the Galois predicate and it has the form:

value
φ :c 1 × c 2 → Bool

Assuming the mediating ties m 1 , ... ,m n ,theformis:

value
φ :c 1 ×

c 2 → m 1 × ... × m n → Bool

The predicate must be explicitly defined; i.e. the function body must be
given. The predicate is utilized in the definition of two dual functions from
sets of objects of the one concepts to the sets of objects of the other, and
vice versa. The dual function pair defines a Galois connection. Thereby, the
characteristics connection is defined. See Sect. 8.
Define an order-preserving connection. Based on classifications of objects
of the two concepts, a connection between the two hierarchies is defined. This
connection shows that specialization of objects of the one concept, implies
specialization of objects of the other concept, if the characteristics connection
is to be maintained. Thereby, the information flow connection is defined.

4 Budgets

A budget is a financial instrument for structuring the works of a project finan-
cially, and for managing and adhering to estimates for the works to be done. By
structuring , we here understand that a budget may designate figures represent-
ing costs of phases, work areas, tasks as well as breaking down of such figures
into sub-phases, sub-work areas, sub-tasks, etc. That is, budgets often reflect a
so-called work breakdown structure .

4.1 Intrinsics

The intrinsics of a budget is that it is a hierarchical structure in the sense that
each figure can be broken down into a set of sub-figure. Each figure in the struc-
ture uniquely identifies a specific subject of expenses. However, figures having
sub-figures, are considered to cover the subjects constituted by the subjects of
the sub-figures.
We model budgets (b:B) as maps from budget figures (bf:BF) to pairs (cf:CF)
of which the first value is the cost (c:C) of the figure and the second is a sub-
budget. A sub-budget is a budget as well. A sub-budget may be empty which
means that the figure is not broken down. Each figure in a budget (including
sub-budgets) uniquely identifies a subject of expenses concerning work, mater-
ial, man-hour costs, etc. That is, it designates the maximum amount of money