Note: This announcement focuses on neurosymbolic reasoning as our FIRST core implementation, establishing the foundation before Darwin-Gödel self-improvement and coordinated space orchestration.

Why Neurosymbolic is First

When we began designing Mamut Lab, we faced a critical architectural question: What should we build first?

Initially, we planned to start with orchestration infrastructure—Coordinated Space components, manoeuvre workflows, distributed systems. But deeper research revealed a fundamental problem: pure LLM orchestrators lack formal guarantees and explainability.

Without neurosymbolic reasoning, we'd build yet another LLM wrapper—fast, but opaque, prone to hallucinations, and impossible to verify. Not what Mamut Lab stands for.

Neurosymbolic reasoning changes everything. It transforms Mamut Lab from "another AI orchestrator" into a provably correct, explainable, trustworthy platform. This is foundational—every future capability builds on this substrate.

What Neurosymbolic AI Actually Is

Neurosymbolic AI combines:

  • Neural Networks (System 1): Pattern recognition, perception, intuition. Fast, but potentially incorrect.
  • Symbolic Reasoning (System 2): Logical inference, formal verification, mathematical proofs. Slow, but provably correct.

Think of it as human dual-process cognition (Kahneman's "Thinking, Fast and Slow") implemented in software. Neural components generate candidates through pattern matching; symbolic components verify correctness through logical reasoning.

The Problem with Pure LLMs

LLM: "Here's code to connect to the database..."
Reality: Hardcoded credentials, SQL injection vulnerability, missing error handling
Frequency: Common enough that GitHub Copilot productivity gains plateau after initial adoption

LLM: "This manoeuvre sequence will work..."
Reality: Violates resource constraints, deadlocks, race condition
Impact: Production failure, manual rollback, hours of debugging

Pure neural approaches lack formal guarantees. No amount of training eliminates hallucinations entirely. Black-box decisions can't be audited. Regulatory compliance requires explainability—pure LLMs can't provide it.

The Problem with Pure Symbolic

Pure symbolic AI (expert systems, logic programming) offers formal guarantees but:

  • Can't learn from data (requires manual rule authoring)
  • Brittle with ambiguity (fails on noisy real-world inputs)
  • Combinatorial explosion (scales poorly to complex domains)

The Neurosymbolic Synthesis

Best of both worlds:

  • Neural: Handles perception, ambiguity, pattern recognition
  • Symbolic: Verifies correctness, provides explanations, ensures safety
  • Integration: Differentiable logic (Scallop) allows end-to-end training

Production-Proven: Real-World Deployments

Neurosymbolic AI isn't theoretical. It's working in production right now:

Amazon Vulcan Warehouse Robots (2025)

  • Deployment: Spokane, WA and Hamburg, Germany fulfillment centers
  • Architecture: Neural vision (object detection) + symbolic task planning
  • Results: Significant error reduction through neural-symbolic verification
  • Scale: 75% of Amazon's 400M unique items, 20 hours/day operation

Why it works: Neural components handle tactile sensing and object recognition (messy real-world perception). Symbolic components ensure task plans satisfy preconditions and resource constraints (formal correctness).

SAP ABAP Code Generation (2025)

  • Problem: LLM hallucinations in code generation
  • Solution: Formal parser integration + knowledge graphs
  • Results: Dramatic accuracy improvement (virtually eliminated hallucinations)
  • Impact: Internal deployment, commercial release planned 2025

Why it works: LLM generates candidate code (neural). Formal parser verifies syntax and semantics against ABAP grammar (symbolic). Knowledge graph checks consistency with codebase patterns (symbolic). Only verified code passes through.

AlphaProof: IMO Silver Medal (Google DeepMind, 2024)

  • Achievement: International Mathematical Olympiad 2024 silver medal (28/42 points, 1 point from gold)
  • Architecture: Gemini LLM (neural intuition) + Lean formal proofs (symbolic verification) + AlphaZero RL
  • Solved: 2 algebra problems + 1 number theory problem (IMO-level difficulty)

Why it works: Neural model proposes proof steps (intuition from learned patterns). Symbolic theorem prover verifies each step is logically sound (formal correctness). Only provably correct proofs accepted.

Mamut Lab Implementation Architecture

Our neurosymbolic implementation builds on production-ready frameworks validated by Amazon, SAP, and DeepMind:

Core Stack (Python Cognition Service)

Scallop (Neurosymbolic Reasoning):

  • Datalog + PyTorch integration
  • Differentiable logic (backprop through symbolic reasoning)
  • 5.3× speedup vs. prior neurosymbolic methods
  • CPU-friendly (no GPU required for MVP)

PyKEEN (Knowledge Graph Embeddings):

  • 40+ embedding models (TransE, RotatE, ComplEx, ConvE, etc.)
  • ArangoDB integration for hybrid queries
  • Semantic similarity + logical reasoning

Z3-Solver (Formal Verification):

  • Satisfiability Modulo Theories (SMT)
  • Prove safety properties (resource bounds, access control)
  • Constraint satisfaction for manoeuvre composition

SymPy (Symbolic Mathematics):

  • Exact mathematical computation (no floating-point errors)
  • Symbolic differentiation, integration, equation solving
  • 100-1000× speedup via lambdify (symbolic → numerical functions)

Integration Pattern: Dual-Process Engine

┌──────────────────────┐      ┌──────────────┐      ┌─────────────┐
│   Claude (Neural)    │ ───→ │  Scallop     │ ───→ │  ArangoDB   │
│   System 1           │      │  (Symbolic)  │      │  (Knowledge │
│   - Generate         │ ←─── │  System 2    │ ←─── │   Graph)    │
│     candidates       │      │  - Verify    │      │             │
└──────────────────────┘      └──────────────┘      └─────────────┘

Workflow:
1. Neural (Claude): Generate manoeuvre/plan
2. Symbolic (Scallop): Verify preconditions, constraints, safety
3. Knowledge Graph (ArangoDB): Retrieve facts, check consistency
4. Feedback: If verification fails, symbolic guides neural retry
5. Execute: Only verified candidates proceed

Implementation Priorities (Phase 1)

The neurosymbolic core (Scallop, PyKEEN, Z3, SymPy) is our highest priority (P-1)— the architectural foundation that all other components (proof kernels, knowledge graphs, synthetic data generation) build upon.

We're implementing three strategic capabilities in parallel:

  • Neurosymbolic reasoning: Differentiable logic + SMT solving (Layer 0)
  • Synthetic data generation: Verified sample generation from axioms using Scallop
  • Knowledge graph reasoning: PyKEEN embeddings + spectral drift monitoring

Self-improvement (Darwin-Gödel) is Phase 2 work (Weeks 17-32), requiring stable neurosymbolic foundation first.

Capabilities This Foundation Enables

1. Synthetic Data Generation (Phase 1 - Current)

Generate training data from axioms without human labels:

  • Axiomatic Theorem Generation: Derive infinite examples from finite rules using Scallop verification
  • Reverse-Process: Differentiate random polynomials → integration training pairs
  • Constraint-Based: Z3 generates test cases satisfying complex constraints
  • Provenance Tracking: Every sample links to source axioms (ArangoDB knowledge graph)

Result: Unlimited training data, guaranteed correctness, no privacy concerns.

2. Knowledge Graph Reasoning (Phase 1 - Current)

Hybrid queries combining symbolic logic + semantic similarity: 

Query: "Find proofs similar to X that depend on theorem Y"

Symbolic Filter (Scallop):
  depends_on(P, Y) → candidates satisfying constraint

Neural Ranking (PyKEEN):
  embedding_similarity(P, X) → semantic relevance scores

Result: Logically valid + semantically relevant

Spectral drift monitoring: Detect knowledge graph degradation using graph Laplacian eigenvalues (λ₂, Cheeger constant). Auto-remediate when drift > 20%.

3. Explainable Decisions (Phase 1 - Regulatory Compliance)

EU AI Act (2024) mandates explainability for high-risk AI systems. Mamut Lab provides:

  • Symbolic Traces: Complete logical derivation for every decision
  • Natural Language Explanations: Convert predicates → human-readable sentences
  • Audit Trails: Store reasoning chains in ArangoDB (immutable, timestamped)
  • Visualization: Proof trees, reasoning graphs

Example: 

Decision: Execute verification "pythagorean_theorem"

Symbolic Trace:
  1. theorem(pythagorean_theorem)
  2. requires_axioms(pythagorean_theorem, [euclidean_geometry])
  3. has_axioms([euclidean_geometry])
  4. ∴ can_verify(pythagorean_theorem)

Natural Language:
  "The system verified pythagorean_theorem because:
   - It's a valid theorem
   - It requires euclidean_geometry axioms
   - The euclidean_geometry axioms are available
   - Therefore, all preconditions are satisfied"

Audit Trail: Stored in ArangoDB with decision ID, timestamp, complete reasoning chain

4. Future: Formal Verification of Self-Modifications (Darwin-Gödel - Phase 2)

Our Darwin-Gödel self-improvement architecture (planned Phase 2, Weeks 17-32) will build on the neurosymbolic foundation to use dual-mode verification:

  • Safety-Critical Properties → Formal Proof Required (Z3, theorem provers)
  • Performance Properties → Empirical Validation (A/B testing, benchmarks)

Example: Before deploying a policy modification, Z3 proves resource consumption stays within budget (formal guarantee). Then empirical testing validates latency improvement (performance optimization).

Result: Self-improvements can never violate safety constraints—mathematical proof required.

Note: Darwin-Gödel requires stable neurosymbolic foundation (P-1), formal verification (P0-P1), and knowledge graphs (P3.5) to be production-ready first. This ensures self-modification has a trustworthy substrate.

Regulatory Context: Why This Matters

EU AI Act (2024): High-risk AI systems require explainability and transparency. Symbolic traces provide automatic audit trails enabling regulatory compliance.

Global Trends: Transparency requirements emerging worldwide. Neurosymbolic AI provides the technical foundation for meeting these mandates through built-in explainability.

Implementation Roadmap

Phase 1: Neurosymbolic Foundation (Weeks 1-16)

P-1: Neurosymbolic Core Bootstrap (Weeks 1-4): Scallop runtime, PyKEEN embeddings, Z3 SMT solver, SymPy symbolic math, neural-symbolic bridge, CEGIS loop (counterexample-guided synthesis)

P0-P3: Formal Verification Foundation (Weeks 1-8): Proof kernel cluster (Lean/Coq), Proof Artifact Repository (content-addressed storage), Type Universe Registry (HoTT/MLTT libraries)

P2.5: Synthetic Data Generation (Weeks 6-9): Axiomatic data generator with Scallop verification, constraint-based sampler (Z3), coverage metrics using generating functions, provenance tracking (ArangoDB)

P3.5: Knowledge Graph Reasoning (Weeks 8-11): ArangoDB graph schema (proof dependencies, type relationships), PyKEEN embedding training pipeline (TransE, RotatE, ComplEx), spectral drift detection (λ₂ monitoring, Cheeger constant), semantic query engine (hybrid AQL + embeddings), auto-remediation workflows

P4-P6: Composition & Verification (Weeks 9-16): Composition planner (categorical semantics), functor catalog (morphism registry), equivalence checker (formal verification pipeline)

Phase 2: Darwin-Gödel Self-Improvement (Weeks 17-32)

Improvement Orchestrator: CEGIS loop for self-modification proposals, proof obligations routing

Empirical Evaluator: Scenario simulations, performance delta measurement, A/B testing

Counterexample Registry: Store counterexamples for neural model retraining, feedback loops

Phase 2 depends on stable Phase 1 foundation. Self-improvement without neurosymbolic verification would risk instability and unsafe modifications.

Why This is Foundational

Every future Mamut Lab capability builds on neurosymbolic reasoning:

  • Darwin-Gödel Self-Improvement (Phase 2): Formal verification ensures safe self-modifications
  • Coordinated Space Orchestration (Future): Symbolic preconditions verify manoeuvre composition
  • Continual Learning (Phase 1): Symbolic invariants prevent catastrophic forgetting
  • Multi-Agent Collaboration (Future): Knowledge graphs enable semantic agent discovery

Without neurosymbolic reasoning, we'd be building purely statistical systems. With it, we're building a provably correct, explainable, trustworthy AI platform.

Phase 1 (current, 16 weeks) establishes the neurosymbolic foundation: differentiable logic, knowledge graphs, synthetic data generation, formal verification infrastructure.

Phase 2 (future, 16 weeks) builds self-improvement capabilities on this stable foundation.

The Vision

Machine intelligence based on mathematical proof, not just statistical learning.

Not replacing neural approaches—combining them. Neural for perception and pattern recognition. Symbolic for verification and safety. Together: the best of both worlds.

This provides Mamut Lab with a fundamentally different architecture: neurosymbolic reasoning as the foundation for trustworthy, long-running AI systems.

Get Involved

Documentation: Read the complete technical architecture

Research Papers: See our comprehensive literature review integrating 90+ research documents

Contact: Questions? info@Mamut Lab.net

This is neurosymbolic reasoning's moment. Production-proven. Regulatory-ready. Mathematically rigorous. And now, Mamut Lab' foundational implementation.