**A set of definitions for MDE**

The core organization of MDE can be captured by a simple set of definitions:

Definition 1. A directed multigraph G = (N

_{G}, E_{G}, G_{G}) consists of a set of distinct nodes N_{G}, a set of edges E_{G}and a mapping function Γ_{G }: E_{G}→ N_{G}x N_{G}Definition 2. A model M = (G, ω, m) is a triple where:

- G = (N
_{G}, E_{G}, Γ_{G}) is a directed multigraph - ω is itself a model, called the reference model of M, associated to a graph G
_{ω}= (N_{ω}, E_{ω}, G_{ω}) - μ : N
_{G}∪ E_{G}→ N_{ω}is a function associating elements (nodes and edges) of G to nodes of G_{ω}(metaElements)

In most technologies, a three level engineering organization has been choosen (see technical spaces).

In MDE, the following is usually assumed:

Definition 3. A metametamodel is a model that is its own reference model (i.e. it conforms to itself).

Definition 4. A metamodel is a model such that its reference model is a metametamodel.

Definition 5. A terminal model is a model such that its reference model is a metamodel.

The three last definitions may be drawn as follows:

The objective now is to define the possible usages of a model. Consequently, in all the following, model will mean “terminal model”.

Definition 6. A system S is a delimited part of the world considered as a set of elements in interaction.

Definition 7. A model M is a representation of a given system S, satisfying the substitutability principle (see below).

Definition 8. (Principle of substitutability). A model M is said to be a representation of a system S for a given set of questions Q if, for each question of this set Q, the model M will provide exactly the same answer that the system S would have provided in answering the same question.

Advertisements