Relating Domain Concepts Intensionally by Ordering Connections - Formal Methods and Hybrid Real-Time Systems - page 188

Relating Domain Concepts Intensionally by
Ordering Connections

Asger Eir

Maconomy Corp.
[e-mail]

Abstract. The present paper suggests a modelling method for relating
domain concepts intensionally. The method is based on modelling con-
cepts formally and establishing two ordering connections between objects
of the concepts. The former connection, we call the characteristics con-
nection . It is a Galois connection and states how objects of the two con-
cepts, describe each other. The latter connection, we call the information
flow connection . It is a connection between classifications of objects of
the two concepts. The connection states how specialization of one kind
of objects, cannot imply generalization of objects succeeding in an in-
formation flow. We put the method to work by modelling the domain
concepts of budgets and project plans, and we establish the two ordering
connections between the models of these. In doing so, we reveal inter-
esting domain knowledge. Hence, we believe that our contribution adds
clarity and transparency to the methodology of domain engineering and
conceptual modelling.

Keywords: Conceptual modelling, Domain Engineering, Intension, Ab-
stract Interpretation, Galois Connection, Classification, Formal Meth-
ods, The RAISE Specification Language (RSL).

1 Introduction

There are many things that can be said about a budget: what the number of fig-
ures is, what the total cost estimate is, etc. These are abstract properties of the
budget and the results of abstract interpretation. Also more complex properties
exist. An example is the property of financially covering the expenses for exe-
cuting a certain project plan. The formal predicate representing this property,
states the condition that project plans must satisfy in order to be executable
within the financial restrictions of the budget. In fact, the predicate states a du-
ality. With it, we can check whether a project plan can be executed within the
financial restrictions of a budget, and we can check whether a budget designates
the necessary expenses for executing a project plan. The reason for this duality
is that budgets describe and determine project plans and project plans describe
and determine budgets. Going either way can be understood as abstract inter-
pretation defined by either of two interpretation functions: one from budgets to
project plans, and one from project plans to budgets. The function pair defines