Ontology

Definition

An ontology is a specification of a conceptualization—it declares what exists and how entities relate. A skill ontology classifies skills and their relationships.

Traditional vs. Generative Ontology

Aspect	Fixed Ontology	Generative Ontology
Entity set	Pre-specified, finite	Potentially infinite, constructively generated
Relations	Declared a priori	Induced by operations
Closure	Extensionally given	Intensionally guaranteed by axioms

In This Project

Induced Ontology Approach

The algebra is prior; the ontology is what the algebra “sees” or “generates.”

Analogous to Klein’s Erlangen program: geometry is the study of invariants under a transformation group. Skill ontology is the study of invariants under skill composition.

Layers of Ontology

1. Algebraic ontology $⟨{\mathcal{S}}_0⟩$ — All possible compositions
2. Realized ontology ${\bigcup }_T{\mathcal{S}}_T^{ϵ}$ — Skills with nonzero fitness
3. Emergent ontology — Skills within model’s emergence threshold

Natural Kinds via Galois Closure

The closed elements of the skills↔tasks Galois connection are the natural kinds—skill-sets “carved out” by task structure.

Terminology Recommendations

Instead of “algebra of skills ontology,” prefer:

• “Compositional algebra of skills” — algebraic structure primary
• “Algebraic framework for skill ontology” — ontology primary
• “Skills calculus” — operational emphasis

Related Concepts

• skills-algebra — The algebraic structure
• mereology — Part-whole relations
• ontological-expansion — Ontology growth
• emergence — Scale-dependent ontology

References

• Clarifying “Algebra of Skills Ontology”
• A mereological reconciliation