Carlos Ramírez Ovalle

Carlos Ramírez Ovalle, Abel Alvarez

Small language models can run locally on consumer hardware, but structured reasoning often pushes users toward repeated sampling or larger models. This article studies a bounded neuro-symbolic alternative for local inference: a model translates a problem into typed finite-domain rules and constraints, a symbolic layer checks traceability and consistency, and a deterministic solver performs the reasoning step. The resulting Verifiable Formalization and Repair pipeline (VFR-LLM) tests when symbolic verification can replace repeated sampling without weakening accuracy. We evaluate it through LM Studio on Apple Silicon, using Qwen3-4B-2507 as the primary model, with Phi-4-mini-reasoning and Gemma-3n-E4B as robustness checks. On 120 generated pure-precedence problems, Qwen VFR-LLM achieves 0.983 accuracy, versus 0.700 for serial self-consistency using one model call instead of five. On a 120-instance BBH-derived extended logical-deduction subset, it reaches 0.933 versus 0.283. The advantage persists against a stronger cost-aware adaptive self-consistency baseline, which lowers sampling cost but not the single-call accuracy gap. Gemma reproduces the same model-dependent boundaries and Phi is negative on typed constraints. The contribution is bounded: finite-domain logic can replace repeated local sampling for some structured tasks, saving model calls and serial latency, with stratum-dependent token savings.

Carlos Ramírez Ovalle

We study a resource-sensitive fragment of the problem of extracting a logical discipline from a class of neural architectures by passing through categorization. The starting point is not a pre-existing logic but a category of zone-labelled parametrised blocks together with a disciplined record of which forms of copying, discarding, and zone coercion are architecturally licensed. From this categorized architecture we read off a subexponential signature and then define a tensorial sequent calculus whose structural rules are indexed by the extracted zones. The paper proves three kinds of results. First, the resulting architectural category is symmetric monoidal. Second, the extracted proof system admits cut elimination. Third, derivations are sound with respect to the licensed categorical diagrams generated by the architectural discipline. The outcome is a theorem-bearing core of the architecture-to-category-to-logic programme: subexponential structure is not postulated in advance but read from categorical data encoding differentiated memory and context behaviour.