Relating Domain Concepts Intensionally by Ordering Connections - Formal Methods and Hybrid Real-Time Systems - page 189

a Galois connection similar to the Galois connection between sets of object and
sets of their common properties in Formal Concept Analysis [1].
In order to create a realistic project plan, a budget is needed and most often
budgeting is a stage preceding project planning because the budget determines
the financial scope of the project plan. If changes are made to a budget, corre-
sponding changes need to be made to the project plan in order for it to still fit
that scope. A general understanding of budgets is that they follow a so-called
work breakdown structure . The structure expresses that general budget figures
are broken down into more specific budget figures. Such a structure can be used
to express the phases, sub-phases, and parallel areas of work, financially. Break-
ing down budget figures or restricting to a sub-set of general figures, narrows
the financial scope of the budget. Hence, we shall say that doing so, special-
izes the budget. A similar perspective can be applied on project plans. Project
plans designate works to be done. Some works may be done in parallel whereas
other works need to be done in sequence. Removing parts of the project plan
narrows the result of executing it. Hence, we shall say that doing so, specializes
the project plan. It appears that specialization of budgets implies specialization
of project plans if the Galois connection between is to be maintained.
The above analysis indicates that there are two interesting aspects in a concept
relation between domain concepts like budgets and project plans. The former
is that budgets describe and determine project plans and vice versa. General-
ized, this is a connection between object sets of the two concepts. The latter
aspect is that budgets and project plans can be ordered respectively and that
specialization in the budget classification implies specialization in the project
plan classification, assuming the first aspect to be maintained.
The two aspects define separate dual connections. The former is a Galois
connection defined by two dually, monotonously, decreasing functions; one from
sets of budgets to sets of project plans, and one from sets of project plans to sets
of budgets. The latter connection is an order-preserving connection between two
classifications; one of budgets and one of project plans.
The two aspects are interesting from a concept modelling perspective for the
following reasons. The Galois connection is the foundation in conceptualizations
where characteristics of objects are modelled by designating their abstract prop-
erties. In our case, the abstract properties are special in the sense that they are
possessed by the objects in virtue of these standing in certain relations to other
objects. That is, the properties are extrinsic properties. We shall say that these
other objects are part of the intensions of the objects in question.
The order-preserving connection ensures consistent concretisation from bud-
gets to project plans. This means that the corresponding concept relation —
when introduced in a conceptual web of concepts related likewise — maintains
the systematics of concretising information from stage to stage in project devel-
opment. The connection adds intensional knowledge as it describes some of the
dynamical characteristics of objects; namely, what effect it has on objects of one
kind to change objects of another.