Assigning delegates to EU working groups
How the MoSeS lecture turns an informal delegation scenario into sets, relations, functions, and precise requirements.
This is a formal-modeling example—not the biblical story of Moses.
Overview
The lecture presents a fictional EU Commission task: form three working groups from delegates sent by Germany, France, Italy, and Austria. Each nation sends three delegates. Each group must contain a delegate from every nation, and its members must share at least one language.
The learning goal is not to guess a real-world roster. It is to make the scenario precise: identify the modeled objects, choose mathematical representations, state the requirements, and be explicit about assumptions the text does not give.
1. Read the informal scenario
The source describes a fabled world with three working groups, four participating nations, three delegates from each nation, and language knowledge that must be taken into account when forming groups.
3 working groups
Modeled as ak₁, ak₂, ak₃, collected in AKS.
12 people in the model
Four nations × three delegates each.
Every nation, in every group
Each working group must include delegates of all four nationalities.
A common language per group
Within each group, at least one language is known by every assigned delegate.
The slides use symbols such as d₁–d₃ for German delegates, f₁–f₃ for French delegates, it₁–it₃ for Italian delegates, and at₁–at₃ for Austrian delegates. The languages are represented by symbols such as s-d, s-f, and s-it.
2. Choose the model’s universe
Give each relevant kind of thing a domain. This separates the objects being modeled from the properties and relationships between them.
AKS = {ak₁, ak₂, ak₃}
// Delegates grouped by nation
D-DEL = {d₁, d₂, d₃}
F-DEL = {f₁, f₂, f₃}
IT-DEL = {it₁, it₂, it₃}
AT-DEL = {at₁, at₂, at₃}
DEL = D-DEL ∪ F-DEL ∪ IT-DEL ∪ AT-DEL
// Nations and languages
NATION = {d, f, it, at}
SPRACHE = {s-d, s-f, s-it}
These are modeling symbols, not the delegates or languages themselves. The slides note that German, French, and Italian are implicit in the scenario’s example setup.
3. Represent properties and assignments
Nationality is an attribute
A total function assigns each delegate exactly one nationality:
For example, a delegate in D-DEL maps to d. This follows directly from the scenario’s division of delegates by sending nation.
Language competence is a relation
The actual language skills are represented by a relation between delegates and languages:
(v, s) ∈ SPRACH-KOMPETENZ ⇔ delegate v speaks language s
The lecture deliberately leaves this relation underspecified: the scenario says to consider language skills, but does not provide an individual skill list. A derived function collects the languages spoken by one delegate:
spricht(v) = {s ∈ SPRACHE | (v, s) ∈ SPRACH-KOMPETENZ}
Group assignment maps a group to a set
The lecture models assignments with a total function whose result is a set of delegates:
zuordnung(ak) = the set of delegates assigned to working group ak
Because the output is a set, a group can contain several delegates. This representation does not, by itself, say that each delegate belongs to exactly one group.
4. State the requirements precisely
Requirement 1 · Every nation is represented
For each working group, the nationalities of its assigned delegates must cover NATION:
NATION ⊆ { nationalität(v) | v ∈ zuordnung(ak) }
Requirement 2 · Each group has a common language
First define the languages shared by all members of a group as an intersection:
The requirement is then that this shared-language set is not empty for every working group:
A valid assignment must satisfy both requirements at once. In the lecture these are represented as requirement relations, ANFORDERUNG₁ and ANFORDERUNG₂; the assignment is acceptable when it belongs to both.
5. Notice what a modeling choice implies
The lecture compares the set-valued assignment with an alternative function:
| Representation | What it means | Modeling consequence |
|---|---|---|
| zuordnung : AKS → 𝒫(DEL) | For each group, return a set of delegates. | Does not itself restrict a delegate to one group or require every delegate to be assigned. |
| traegt-bei : DEL → AKS | For each delegate, return one group. | As a total function, it forces every delegate into exactly one group—an extra constraint not stated in the original scenario. |
This is why the course favors the first representation for the initial model: it avoids adding assignment restrictions absent from the scenario.
Extra conditions can be added deliberately
The lecture then considers additional possible requirements: no delegate appears in more than one group, and every delegate appears in at least one group. These are sensible constraints for some interpretations, but they should be marked as extra requirements rather than smuggled into the base model.
With 12 delegates, 3 groups, and every group required to include all 4 nationalities, requiring every delegate to be assigned and no delegate to appear twice forces exactly one delegate of each nationality into each group. That conclusion depends on those added conditions; it does not follow from the two original requirements alone.
6. What the scenario leaves open
The lecture emphasizes that the model is parametric in both the language-competence relation and the group assignment. The problem statement does not tell us which individual speaks which language, nor does it provide a final roster.
Who speaks what?
SPRACH-KOMPETENZ is declared, but no concrete pairs are supplied.
Who goes in which group?
zuordnung is a candidate assignment to be constrained or found.
So this model expresses how to test an assignment; it does not by itself produce a unique assignment. Concrete delegate skills or more assumptions would be needed to calculate one.
Takeaways
Course source
Your document: Module02 – Formale Modelle und Formale Modellierung, MoSeS, WiSe 2026/27, lecture slides. The “Arbeitskreise der EU” scenario and formalization are covered across the slides/pages on the scenario, domains, language competence, attributes, requirements, and assignment model (including slides 13–44).
The slide deck notes that the scenario is based on Kastens and Kleine Büning, Modellierung (2008). This page is an explanatory companion to the material in your documents.