Long description

• Experiential Learning: Rules generated by agents exploring and interacting with their environment, such as in the AIRIS system, where agents autonomously generate and adapt logic rules based on sensory inputs and actions.
• Higher-Order Reasoning: More complex logic rules provided by human users, allowing systems to engage in abstract or hierarchical reasoning tasks.

1. A comprehensive survey and analysis of current neural-symbolic DNN architectures capable of embedding logic rules. Researchers are expected to evaluate the strengths and limitations of each architecture, particularly with respect to handling dynamic system behaviors across spatio-temporal scales.
2. Proof of Concept (POC). We can easily see two ideas for POCs:
   1. Use PyNeuraLogic to demonstrate how logic rules can be embedded within a chosen DNN architecture. For example, simple logic rules derived from AIRIS could be embedded into GNNs using PyNeuraLogic, allowing the system to reason over the outputs of those GNNs, or LLMs. This POC would show how such architectures improve both experiential learning and/or higher-order reasoning. 
   2. As detailed in “KAN: Kolmogorov–Arnold Networks”, KANs operate quite differently than does PyNeuraLogic. KANs are quite interesting in their own right and appear to be more effective at representing certain types of functions, especially those of interest to the mathematical physics community, than do MLPs. Being built upon continuous splines, KANs can help bridge the discrete-continuous divide. They can also provide excellent human interpretability, yet sometimes rely on post-processing by either an automated symbolic regression step or, alternatively, human interaction to do so. One idea for a POC involving KANS would be to explore how well KANs could be used to ingest accurate and explainable DNNs in Hyperon. As one example, perhaps one could use KANs to create a predictive model for real-time energy consumption in a smart grid. The goal could then be to demonstrate how KANs could improve accuracy and explainability of the model, particularly in handling dynamic continuous data (e.g. fluctuating energy usage) alongside discrete events (e.g. switching energy sources). Another possibility could involve market predictions.

• Comprehensive Survey and Evaluation: A detailed evaluation of different neural-symbolic architectures, including PyNeuraLogic, KANs, and others, with a focus on their ability to embed logic rules and enhance reasoning capabilities.
• Architectural Comparisons: A comparison of how these architectures perform in embedding rules, addressing challenges in scalability, flexibility, and integration with complex systems across multiple spatio-temporal scales.
• Proof of Concept (POC): A POC in the MeTTa language that demonstrates the feasibility of embedding logic rules into DNNs and applying reasoning over their outputs, using systems like AIRIS or user-supplied rules.
• System Dynamics Demonstration: Evidence that the approach can drive interesting dynamics across multiple scales, showing improvements in reasoning and decision-making in dynamic environments.
• Explainability: Explain how different architectures improve human interpretability and explainability of AI systems.
• Learning from Small Data: Compare how different  architectures can learn from small data using symbolic knowledge and reasoning.
• Multiparadigmality: Bridge the gap between data-driven and symbolic reasoning.
• Structured Learning: Evaluate how different architecturea can solve problems in domains in which structured learning is critical (e.g. medical ontologies).