How to experiment with neuro-symbolic AI?

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Hey all! I want to start testing neuro-symbolic AI vs. LLM's and want to know how to get into this. As I understand it, Claude Code, does this, but are there ways to use it locally?

How does it work under the hood? I know LLM's involve tokens, embeddings, weights and transformers. How does the symbolic part of it change it?

Thanks!