Enforcing Logical Invariance in Large Language Models via Symmetry Pair Training

Despite their scale, Large Language Models (LLMs) frequently exhibit \emph{logical fragility}---a phenomenon wherein minor linguistic permutations of the same logical premise yield contradictory outputs. We introduce \textbf{Contrastive Consistency Tuning (CCT)}, a training framework that enforces logical invariance in a model's latent space by leveraging semantically equivalent but structurally distinct \emph{Symmetry Pairs}. CCT augments a standard cross-entropy objective with a contrastive consistency penalty that minimises representational divergence between logically equivalent prompts. To generate training data at scale, we present the \textbf{Symmetry Engine}, an automated pipeline of five logical transformation rules applied to FOLIO and ProofWriter benchmarks. Evaluated on Llama-3 (8B) and Mistral-7B, CCT reduces the \emph{Contradiction Rate} (CR) by 19--20 percentage points over vanilla fine-tuning baselines while preserving overall accuracy. Crucially, we demonstrate that frontier models such as GPT-4o and Claude~3.5~Sonnet exhibit non-trivial contradiction rates (${\sim}30\%$), suggesting that logical fragility is not resolved by scale alone.