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Knowledge Database

A comprehensive, structured knowledge base for LLM Skills Research, containing formal definitions, mathematical structures, and research applications from the skills ontology.

Overview

This knowledge database provides a systematic organization of concepts related to:

  • Skills: Fundamental capabilities in AI systems
  • Metaskills: Higher-order skills for skill manipulation
  • Mathematical Structures: Formal frameworks (semigroups, lattices, fixed points)
  • Research Applications: Skill emergence, composition, and self-improvement

Structure

knowledge-database/
├── concepts/               # Structured concept files
│   ├── index.md           # Main navigation and overview
│   ├── core-concepts/     # Fundamental definitions (9 files)
│   ├── mathematical-structures/  # Theorems and proofs (3 files)
│   └── research-applications/    # Practical applications (2 files)
├── analysis-data.json     # Repository metadata
└── README.md             # This file

Quick Start

Start with the Concept Index for navigation and overview.

Core Learning Path

  1. Skill (𝒮) - Start here to understand the basic unit
  2. Composition Operator (∘) - How skills combine
  3. Metaskill (𝓜) - Skills about skills
  4. Skill Composition Semigroup - Mathematical foundation
  5. Skills Algebra - Practical framework

By Interest

For Theorists:

For Practitioners:

For Researchers:

Content Quality

Each concept file includes:

  • ✅ YAML Frontmatter: Metadata, tags, and relationships
  • ✅ Formal Definitions: Mathematical notation with LaTeX
  • ✅ Key Properties: Essential characteristics and constraints
  • ✅ Research Context: Applications and use cases
  • ✅ Cross-References: Links to related concepts
  • ✅ Open Questions: Active research directions

Mathematical Notation

The knowledge base uses standard mathematical notation:

  • 𝒮: Skill space
  • 𝓜: Metaskill space
  • ∘: Composition operator
  • ↓: Decomposition operator
  • ⊙: Metaskill application
  • ≼: Partial order (prerequisites)
  • Φ: Agent fitness function
  • φ: Skill fitness function

See LaTeX Guide for rendering.

Statistics

  • Total Concepts: 14
    • Core Concepts: 9
    • Mathematical Structures: 3
    • Research Applications: 2
  • Source: ontology/skills-ontology.md
  • Format: Markdown with LaTeX
  • Extraction Date: 2025-11-21

Research Goals

Understanding and formalizing:

  1. How skills emerge in LLMs
  2. Composition and decomposition of skills
  3. Metaskills for self-improvement
  4. Skills algebra as alternative to formal verification
  5. Building self-improving agents through skill composition

Usage

For Research

Browse concepts to:

  • Find formal definitions for your work
  • Identify open research questions
  • Understand relationships between concepts
  • Discover mathematical frameworks

For Development

Use concepts to:

  • Design skill-based agent architectures
  • Implement composition mechanisms
  • Evaluate agent capabilities
  • Build self-improving systems

For Documentation

Link to concepts when:

  • Explaining technical approaches
  • Citing formal definitions
  • Discussing theoretical foundations
  • Planning research directions

Maintenance

This knowledge base is:

  • ✅ Version Controlled: All changes tracked in Git
  • ✅ Structured: Consistent format across all files
  • ✅ Cross-Referenced: Concepts link to related concepts
  • ✅ Open: Contributions welcome

Contributing

To add or update concepts:

  1. Follow the established YAML frontmatter format
  2. Include formal definitions with proper LaTeX notation
  3. Add research context and practical applications
  4. Cross-reference related concepts
  5. Include open research questions
  6. Update the index.md file

Deployment

The knowledge database is automatically deployed to a Quartz-based website via GitHub Actions when merged to main.

Source Material

All concepts are extracted from:

License

This knowledge base is part of the LLM Skills Research project and is open for academic collaboration and contribution.

Last Updated: 2025-11-21
Version: 1.0
Status: ✅ Complete extraction from skills ontology

Graph View