This paper presents a unified formal system combining T-Logic—a six-phase dialectical reasoning model—with Recursive Calculus, an analytic framework for iterative transformation. We define a transformation operator that encapsulates Expansion, Contraction, Inversion, Transformation, Reflection, and Emergence, and show that under contraction conditions, this operator converges to a unique fixed-point belief state. The resulting system models recursive reasoning processes that are logically sound, mathematically convergent, and applicable to domains such as machine learning, economic equilibrium modeling, and self-correcting epistemic systems. We provide formal definitions, axioms, and theorems with rigorous proofs, demonstrating that dialectical reasoning can be expressed as a contractive process in a Banach space. The work contributes to logic, epistemology, and systems theory by offering a recursive framework that balances adaptation with convergence.
\nKeywords:
\nrecursive logic, T-Logic, recursive calculus, dialectical reasoning, fixed-point theorems, convergence, epistemic systems, Banach space, neural networks, economic equilibrium, paraconsistency, systems theory
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