Traffic signal control is a challenging sequential decision-making problem requiring a balance between throughput, vehicle delay fairness, signal stability, predictable switching, and emergency vehicle prioritisation. Existing reinforcement learning (RL) approaches often rely on predefined objectives and offer limited adaptability to changing operational priorities. They may also generalise poorly across geometrically equivalent intersections. To address these limitations, SIGMA (Symmetry-aware, Intelligent, Geometric, Multi-faced Adaptive traffic control) is proposed as a multi-faced RL framework augmented with a large language model (LLM) for dynamic objective adaptation and orientation-invariant policy learning. Natural language emergency instructions are translated into priority vectors that guide a multi-faced actor-critic controller. Symmetry-aware rotational augmentation supports transfer across homogeneous four-way intersections, while an offline-to-online learning strategy enables stable initialisation and adaptation to evolving traffic conditions. Structural properties concerning emergency service levels, graceful degradation under LLM failure, and sensitivity to traffic demand perturbations are established, alongside bootstrap-based statistical validation. Experiments in SUMO across four urban intersections modelled on Kolkata traffic scenarios compare SIGMA with fixed-time, actuated, and Deep Q-Network controllers. Reductions in average waiting times, emergency waiting times, and queue lengths are observed, alongside improved traffic throughput. Empirical reliability and ablation analyses further assess robustness to component failures and geometric orientation. SIGMA integrates language-guided objective adaptation, multi-faced policy learning, and statistical reliability assessment into an adaptive framework for intelligent traffic control.

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