Structured Abductive-Deductive-Inductive Reasoning for LLMs via Algebraic Invariants

This research introduces a symbolic reasoning scaffold to address systematic limitations in LLMs' structured logical reasoning, such as conflating hypothesis generation and propagating weak inferences. It operationalizes Peirce's tripartite inference, enforcing logical consistency through algebraic invariants, notably the 'Weakest Link bound' to prevent conclusion reliability from exceeding its least-supported premise.