Edge user/service scheduling governs where and how AI services are executed under limited communication and computing resources. Existing edge scheduling frameworks typically assume numerically specified service requirements, such as latency bounds and energy budgets. However, users often express ambiguous and context-dependent expectations in natural language, creating a gap between user intent and scheduling decisions. We propose semantic contract-guided edge potential scheduling (STEPS), a natural language-driven framework that introduces semantic contracts as executable interfaces between user-side semantics and edge-side decisions. A large language model (LLM)-assisted semantic parser extracts service requirements and raw confidence scores from natural language requests. Confidence calibration and interpretable mapping rules convert these outputs into preference weights, fulfillment bounds, and semantic uncertainty. STEPS formulates intended per-slot edge scheduling as an exact potential game for execution-node selection, computing-resource provisioning, and bandwidth allocation, followed by capacity-feasible resource realization. Fulfillment-driven feedback signals enable adaptive scheduling under evolving service and network conditions. We establish the existence of pure-strategy Nash equilibrium, prove finite-step convergence of uncapped strict best-response dynamics, and characterize the boundedness of projected adaptive-control parameters. Experiments under synthetic and Melbourne-based hybrid settings demonstrate improved contract fulfillment and reduced service loss relative to several adapted benchmarks. Post-drift evaluations further show that feedback adaptation improves fulfillment and admission coverage under the tested conditions.

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