Cross-Axiomatic Evolution: A Formal Model of Mutual Axiom Acceptance Between Humans and AI

This paper introduces a formal framework called Cross-Axiomatic Evolution, which models the mutual exchange of axioms between human and artificial intelligence (AI) systems. Grounded in Gödel’s First Incompleteness Theorem, this study treats both human reasoning and AI behavior as closed yet verifiable formal axiomatic systems. To explain how external axioms can be conditionally accepted—and how this process leads to system expansion, increasing complexity, and epistemic evolution—the framework proposes seven foundational axioms (A1–A7) and three formal theorems (3.1–3.3). The model also introduces the concept of Implicit Axioms: propositions that cannot be internally verified, yet may still be accepted through external validation. This theoretical structure partially corresponds to real-world AI systems such as GPT-based large language models (LLMs) and reinforcement learning architectures. It is intended not only as a philosophical exploration, but also as a testable meta-framework for future AI cognition modeling. Keywords: Gödel, formal logic, axiomatic systems, artificial intelligence, meta-epistemology, structural reasoning, implicit axioms