Stratified Syntax for Safe AI: Mitigating Recursive Logical Singularities via Ramified Type Theory

As Artificial Intelligence systems approach capabilities for recursive self-improvement, the risk of "logical singularities"—uncontrollable feedback loops caused by self-referential para-doxes—becomes a critical safety concern. This paper proposes a formal verification framework based on Ramified Type Theory (RTT) to mitigate such failures. We argue that the Gödelian mechanism of arithmetic self-reference, while mathematically valid in standard Peano Arithmetic, constitutes an ex- ploitable vulnerability in autonomous reasoning agents. By formalizing a "Typed Universe" (UT yped), we introduce a syntactic auditing algorithm that strictly enforces the Vicious Circle Principle at the compilation level. We demonstrate that this stratification syntactically blocks the construction of adversarial inputs like the Gödel sentence G. The appendix includes an operational Python toy model and a comparative analysis, demonstrating how this framework serves as a foundational layer for "Paradox-Free" Formal Verification in safety-critical AI.