This initial milestone will establish the theoretical and architectural foundation for the project. We will survey the state-of-the-art in neural-symbolic systems, including PyNeuraLogic, Kolmogorov–Arnold Networks (KANs), DeepProbLog, and related frameworks. The objective is to evaluate their strengths for embedding logic into DNNs and assess their suitability for integration with the OpenCog Hyperon architecture. We will design Atomspace schemas to represent molecular/physics simulation states and draft the logic embedding strategy for both experiential (AIRIS-style) and higher-order (expert-supplied) rules. A PRIMUS-aligned interaction diagram will be drafted to show how neural models will interoperate with MeTTa-based inference.

A comparative report on neural-symbolic DNN frameworks with evaluation criteria. A design document detailing the architecture of the symbolic neural learning system. Initial MeTTa rule structure and Atomspace schema drafts to encode physics/molecular environments. A prototype test of MeTTa executing logic over placeholder atoms to confirm pattern-matching compatibility. Annotated mapping of how experiential and higher-order rules will be encoded and referenced within Atomspace and queried via MeTTa.

$8,000 USD

Completion of literature and framework survey with justified framework selection. Internal validation that Atomspace structures can represent simulation states and rules appropriately. MeTTa test script demonstrates pattern-matching over symbolic atoms. Technical plan reviewed and verified for compatibility with PRIMUS/Hyperon conventions.

This milestone focuses on the implementation of two neural-symbolic prototype models: one using PyNeuraLogic and the other based on KANs. Both models will be trained on ab initio data generated via molecular or physics simulations. Symbolic rules — both experiential and higher-order — will be embedded into each architecture. Simulation states will be represented in Atomspace, and rule-driven inference will be handled through MeTTa. Prototypes will be integrated with MeTTa to demonstrate symbolic filtering, constraint enforcement, or inference guidance over simulation episodes. Experiential rule learning will be mocked via scripted rule induction, mimicking AIRIS-like patterns.

A PyNeuraLogic-based GNN that respects one or more embedded MeTTa-derived rules. A small KAN-based model that switches behavior based on symbolic logic conditions. A simulation log-to-Atomspace parser to automatically convert simulation output into symbolic atoms. Sample rules injected via MeTTa, including one experiential (pattern-mined) and one higher-order (hand-specified). Demonstration code and documentation showing end-to-end simulation → symbolic inference → neural model interaction. A Jupyter notebook or video walkthrough illustrating symbolic intervention improving model behavior.

$16,000 USD

Both neural models (PyNeuraLogic and KANs) are fully functional with symbolic input incorporated. Successful interaction loop between MeTTa-inferred logic and neural model output demonstrated. Model performance reflects logic influence (e.g., better generalization or constrained predictions). Clear evidence that symbolic reasoning has modified model behavior in at least one test case. All code and interfaces are documented and reproducible in a testing environment.

The final phase will benchmark the symbolic neural architectures against baselines, evaluating generalization under small-data regimes and reasoning fidelity. Quantitative metrics (accuracy, data efficiency, rule compliance) and qualitative analysis (explanation clarity, traceability of inference) will be compiled. A final demonstration will show integrated use of Atomspace, MeTTa, and symbolic-enhanced neural models for causal prediction in physics/molecular simulations. Documentation will cover reproducibility and offer integration guidance for PRIMUS and Hyperon modules, including an implementation plan for future scaling or incorporation into AGI kernels.

Benchmark report comparing performance of symbolic vs. non-symbolic models on multiple simulation tasks. Evaluation of symbolic reasoning accuracy, generalization to unseen scenarios, and learning efficiency from small data. Fully annotated codebase with modular components for Atomspace interaction, MeTTa rules, and neural models. Integration notes detailing how to extend the logic engine as a skill/module in PRIMUS. Recorded demo or walkthrough showing reasoning over Atomspace atoms and corresponding neural output. Delayed open-source release plan with defined licensing and community engagement strategy.

$16,000 USD

Symbolic models outperform baselines in accuracy and/or learning efficiency with limited training data. At least two tasks show clear benefits from logic-guided inference (e.g., lower loss, logical rule compliance). Demonstrated compatibility with Hyperon cognitive patterns (grounded atoms, MeTTa queries, multi-agent cognition). Documentation enables other teams to understand, reproduce, and build upon the project.