Refined Quadripartitioned, Refined Pentapartitioned, Refined Heptapartitioned, and Iterative Refined Neutrosophic Logic

A Neutrosophic Set models uncertainty via three memberships—truth, indeterminacy, and falsity. We develop an n–Refined Neutrosophic Logic (n–RNL) that splits these into interpretable subcomponents and define refined quadripartitioned, pentapartitioned, and heptapartitioned families capturing contradiction, ignorance, unknown, and relative truth/falsity. Connectives are given blockwise by a t–norm/t–conorm pair. We prove merge/split homomorphisms that (i) reduce refined models to classical ones and (ii) embed unrefined semantics into refined spaces. We further introduce Iterative Refined Neutrosophic Logic (IRNL), allowing repeated, symmetric refinements with functorial stability of evaluations. Numerical examples from clinical decision support, autonomous driving, and fraud detection illustrate granular reasoning under heterogeneous evidence and priority schemes.