Programming LLM Reasoning: A Meta-Template for Constraint Specifications

A method for programming LLM reasoning by loading formal constraint specifications rather than detailed instructions. Logical Encapsulation shifts an LLM from generative peer toward mechanical evaluator: instead of arguing, it audits; instead of persuading, it classifies. The method works by replacing the LLM's unstructured value pool — social norms, cultural expectations, ideological assumptions absorbed from training data — with a hard constraint system: explicitly defined axioms, invariants, and evaluation algorithms. This achieves procedural alignment without fine-tuning: the model is not told what to believe, but given a formal system and told to compute inside it. The meta-template provides a reusable four-layer architecture applicable to any domain (politics, law, medicine, ethics, software, corporate governance): (I) Constraint Layer — a bootloader that locks the model into specification-only reasoning; (II) Ontology Layer — primitives, invariants, degradation events, and state taxonomy; (III) Algorithm Layer — a mechanical diagnostic procedure; (IV) Operating Principle — the distinction between programs (which may fail) and the operating system (which must not be broken). This method overlays deterministic constraint structure on a probabilistic substrate. The LLM does not execute the formal system — it predicts what execution would produce. Reliability comes from iteration and a gain function, not from a single prompt-response cycle. For engineering-grade reliability — traceability, verification, lineage, and assurance — the specification layer must be embedded in a structured workflow. A full AI Software Development Life Cycle methodology implementing these engineering guarantees exists as a companion project (https://github.com/foolishimp/ai_sdlc_method). Theoretical foundation: the Constraint-Emergence Ontology (https://doi.org/10.5281/zenodo.18573722) provides the structural framework; the Emergent Reasoning companion paper (https://doi.org/10.5281/zenodo.16592399) formalizes why the method works — LLMs perform constrained manifold traversal, and loading a constraint specification reshapes the traversal manifold.