Formalization of Natural Deduction System in Proposition Calculus

With the rapid development of artificial intelligence research, the relationship between mathematical logic and arti-ficial intelligence is becoming increasingly close. Mathematical logic is one of the cornerstones of artificial intelligence. At present, consolidating the theoretical foundation of artificial intelligence will provide guarantees for the development of artificial intelligence technology. Proposition calculus is the most fundamental in mathematical logic, with two types: axiom sys-tems and natural deduction systems. Axiom systems start from axioms, while natural deduction systems start from reasoning rules, and the derivation process tends to natural ideas. This article establishes a natural deduction formal system for propo-sitional calculus using the theorem prover Coq, and verifies the equivalence between natural deduction systems and axiom systems.