AIOS: AI Operating System
The Biological Intelligence Layer
Mathematical Biology for AI
AIOS is the biological intelligence layer of LATTICE—the whole cognitive system. Its parts are: COE (the brain/orchestrator), CNS (neural routing), ANS (autonomic stability), and SNS (somatic actuation). The mathematics below is sourced from our AIDF and TAI proof documents.
Core Components
🧠 COE: Cognitive Orchestration Engine
∇ₓJ(x*) + ∑ⱼ λⱼ*∇gⱼ(x*) + ∑ₖ μₖ*∇hₖ(x*) = 0
- Decision orchestration via optimization (KKT stationarity)
- Learning from feedback with primal–dual updates
- Context preservation with holographic memory
🔗 CNS: Cognitive Neural System
Determinism: C → C₁ ∧ C → C₂ ⇒ C₁ = C₂
- Signal routing with deterministic small-step semantics
- Distributed coordination via verified transitions
- Real-time adaptation to load
🛡️ ANS: Autonomic Nervous System
dC/dt = -γC + ∑ᵢ Aᵢ(◊ᵢ) + ℰ[Ψ]
- Homeostatic control via resonance and emergence
- Forgetting and amplification balances (γ, Aᵢ, ℰ)
- Stability from field dynamics
🤖 SNS: Somatic Nervous System
xₜ₊₁ = f(xₜ, uₜ) + wₜ; yₜ = g(xₜ) + vₜ
- Actuation and control under discrete-time dynamics
- Traceable outputs with denotational meaning
- Closed-loop execution with proofs
Biological Principles
Integration with LATTICE
AIOS sits at the top of the LATTICE stack, providing the intelligence that guides execution. It receives compositional intents from LQL, orchestrates their execution through LEF particles, and learns from the outcomes to continuously improve.
Intent (User)
↓
LQL (Chemistry Layer)
↓
AIOS (Biology Layer) ← Learning Feedback
↓
LEF (Quantum Layer)
↓
Execution (Reality)Real-World Applications
Autonomous Decision Making
AIOS orchestrates via proof-backed LQL, LEF, AIUCP, and memory
Adaptive Learning
Continuous improvement through biological feedback
Fault Recovery
Self-healing through redundant neural pathways