Relating Domain Concepts Intensionally by Ordering Connections - Formal Methods and Hybrid Real-Time Systems - page 190

In the cross-disciplinary areas between computer science and application do-
mains, modelling of domain concepts and defining their relations, is an essential
process for founding computerized management. Also, it is essential for reaching
a clarification of the domain in general. However, there is a lack of methods for
defining such relations. Consequently, the domain engineering approach may be
quite informal and implicit; or even given up.
In this paper, we outline a method for relating domain concepts based on
formalizations of these concepts. The method establishes concept relations on
(i) a Galois connection between object sets of the concepts, and (ii) an order-
preserving connection between classifications of objects of the concepts. In order
to put the method to work, we model the domain concepts of budgets and
projects plans formally, and we establish the Galois connection and the order-
preserving connection between these concepts 1 . Founding a concept relation on
the two ordering connections, we believe makes the concept relation more rigour
than a relation simply claimed to hold between two concept names. It is so, as
it includes the semantic aspects of characteristics and change effects. Hence, we
consider the utilization of the two kinds of ordering connection as a contribution
to the current debate on the methodology of domain engineering in computer
science. In essence it puts the semantic question of what it means for two domain
concepts to relate, on the agenda — a question which is present in almost any
development of software and IT systems.
Throughout the paper, we use The RAISE Specification Language (RSL) to
express the formal models, relations and conditions [4,5]. However, effort has
also been made to informally express the understanding and intuition behind
the models.
2 Domain Engineering
In the paper, we shall assume the following understandings of concept relations:
Definition 1 (Concept Relation). By a concept relation ,weunderstanda
relation between two concept names, implicitly or explicitly stating the criteria
for objects of the concepts to relate.
Hence, when we talk about a concept relation, we also talk about a relation
between the objects of the concepts.
Definition 2 (Implicit Concept Relation). By an implicit concept relation ,
we understand a concept relation for which the criteria are implicitly or infor-
mally expressed.
Definition 3 (Explicit Concept Relation). By an explicit concept relation ,
we understand a concept relation for which the criteria are explicitly and formally
expressed.
1 Pre-studies have been done in [2] and [3].