GitHub-Formalizing the Strong Goldbach Conjecture for AI(HOL,Standard Semantics)

Semantic formalization of the Strong Goldbach Conjecture using Second-Order Logic (SOL) and Higher-Order Logic (HOL), designed for AI reasoning and logic modeling.

This repository presents two semantic logic frameworks that reformulate the Strong Goldbach Conjecture using:

• Second-Order Logic (SOL): using relational set quantifiers
• Higher-Order Logic (HOL): using functional and predicate types

These formulations are designed to be:

• Logically closed
• Semantically bounded
• AI-compatible for formal reasoning, rule induction, and logical validation

The logical structures of the Strong Goldbach Conjecture are organized as follows:

The logical structures of the Strong Goldbach Conjecture are organized as follows:

• Logic/strong-goldbach-SOL-semantic-formalization.md
  Semantic formalization of the conjecture in Second-Order Logic (SOL) under standard semantics.

• Logic/strong-goldbach-HOL-semantic-structure.md
  Logic structure of the conjecture in Higher-Order Logic (HOL) including function-based mapping formulation.

Both are implemented via GPT + GSML (Light) architecture.

• Strong Goldbach Conjecture: Every even number greater than 2 is the sum of two primes.
• Semantic closure: All definitions are self-contained within logic domains
• No proof assumed: This is a semantic structure, not a formal proof
• Standard semantics: Full quantifier scope, no Henkin interpretation
• AI-Ready: Structured for use in AI logic engines and formal knowledge systems

This project is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0).
You may share and adapt the work, with attribution to the original author.

Author: JiaQing Chen
Date: 2025/07/29