Skills

Definition

A skill is a discrete, identifiable capability that can be applied to tasks. Skills can be composed to form complex capabilities.

In the Literature

Definitions by Paper

Paper	Definition	Granularity
Arora & Goyal	Node in skill graph; comprehension requirement for text	Abstract
SKILL-MIX	Wikipedia-documented language/reasoning skill	Named (101 skills)
Didolkar et al.	LLM-assigned label (e.g., “circle_properties_area_calculation”)	Fine → Coarse
Fan et al.	ICL capability on a function class	Functional
Michaud et al.	Quantum (discrete knowledge chunk)	Discrete module
SELF	Meta-skill: Self-feedback + Self-refinement	Procedural

Key Distinctions

1. Basic skills — Primitive capabilities (our ${\mathcal{S}}_0$)
2. Composite skills — Combinations of basic skills
3. meta-skills — Skills for operating on skills

In This Project

Our skills-algebra formalizes skills as elements of a monoid $(\mathcal{S},\circ ,1)$:

• Composition $\circ$ combines skills
• Identity $1$ is the null skill
• Fitness function $\varphi (S,T)$ measures skill-task fit

Skills have both:

• Mereological structure — Part-whole relations (constitutive)
• Algebraic structure — Composition relations (operational)

Related Concepts

• composition — How skills combine
• meta-skills — Higher-order skills
• skills-algebra — Formal framework
• ontology — Skill classification
• emergence — How skills appear with scale

References

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