ULOGIC (Universal Logic Language) PARADIGM for AI

Current paradigms of mathematical formalization (based on Dependent Type Theory like Lean) present a fundamental barrier for Artificial Intelligence: grammatical dissonance. Encoding informal mathematical discourse into a language with a radically different grammar (Lean or similar) does not preserve meaning, but rather alters it. This “Representational Rupture” crystallizes ideas rigidly, blocking the AI’s ability to detect analogies and intuitions necessary for discovery. We propose ULOGIC, a new paradigm based on an underlying grammar isomorphic to semi-formal mathematical language (using nested syntactic chains HAL-Chains ”Headed-Atomic-List”). ULOGIC allows everyday semi-formal mathematical expression to be computationally verifiable without suffering the semantic distortion of translation into distant logical code, enabling a new generation of neuro-symbolic AI systems capable of exact reasoning, capable of reusing knowledge, and ultimately capable of acting as reliable AI agents for discovery in science and industry.