Information Technology Reference
In-Depth Information
The notion of Galois connections is a mathematical concepts which founds
a variety of applications. The application we shall consider here is the Galois
connection between of objects and their common properties; a central subject
in Formal Concept Analysis [1]. Consider the set of physical objects in a living
room. For each object — chair, picture, table, candlelight, etc. — we can observe
its properties like colour, weight, material, dimensions, length, etc. The notion
of properties is here a wide notion; any predication of an object will do. Pick
a subset of the objects and list the set of their common properties. That is,
the properties that all objects in this set have. If we extend this set with more
objects, we will either get a smaller set of common properties or have the same
set. Similarly, we may pick a subset of properties and list the set of objects
all having these properties. If we extend this set with more properties, we will
either get a smaller set of objects or have the same set. Between objects and
their common properties there is a Galois connection [1]. This connection is
fundamental in all conceptual modelling and classification.
Now, consider another kind of objects and another kind of properties. The
objects may be more abstract rather than physical. Examples of such kinds
of objects are (from the domain of project planning): Budgets, project plans,
resource allocations, plan executions, products, services, collaborations, etc.; ba-
sically any kind of thing or phenomena existing or potentially existing in the
domain. Similarly, the properties of these objects may be abstract. Just as we
can observe the colour and texture of a physical object, we can determine the
relations to which an object stand to other kinds of objects; i.e., the extrin-
sic properties in addition to the intrinsic properties. As an example, we may say
that a budget relates to the project plans that are executable within the financial
restrictions of the budget; and vice versa.
Defining a Galois connection between two domain concepts can be an im-
portant foundation for conceptual domain modelling as it defines the charac-
terisations of domain objects based on their relations to other objects. For this
reason we shall say that the concept connection is intensional . The connection is
a characteristics connection . Furthermore, a Galois connection provides a range
of theorems that are convenient in context of model checking or other kinds of
analysis of a domain model.
3.2 The Order of Information Flow
In order to carry out a project, a project plan is needed; and in order to produce a
project plan, a budget is needed. This exemplifies that some kinds of information
are input knowledge to the process of creating other kinds of information.
Now, consider a collection of domain concepts that are placed in a hierarchy
describing the order in which information is created and used through stages of
projects. If changes are made to one object (e.g. a budget is changed), it may
influence other objects (e.g. put or release restrictions to a project plan). In order
to formalize this, we shall consider changes to objects as either specializations
or generalizations within classifications of the objects for each domain concept.
For a budget, we may increase or decrease a budget figure, introduce a new or
 
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