Urban multi-energy communities face coupled carbon regulations, volatile markets, and uncertain renewable generation, creating a need for decision systems that adapt beyond static optimization. This study develops an adaptive computational knowledge-based expert system for coordinating electricity, heat, gas, hydrogen, and carbon flows under uncertainty. The architecture combines carbon accounting and tiered carbon trading with a joint conditional value-at-risk and chance-constrained decision structure. It comprises three intelligent cores: an adaptive knowledge-updating layer for dynamic parameter refinement, a digital-twin-based state inference engine for interconnected energy hubs, and a synchronization core that aligns operational decisions with observed system conditions. Distributed coordination is implemented through a decentralized alternating direction method of multipliers framework, supporting scalable reasoning while preserving modularity. Carbon trading is treated as a policy-sensitive decision component, enabling reward–penalty signals to influence operational inference rather than acting as a simple linear cost. The integrated risk-aware engine evaluates feasible schedules under renewable uncertainty and market volatility. Simulations for an energy-intensive industrial community show that the system reduces total operating cost by nearly 20% relative to a carbon-trading-only configuration, lowers carbon emissions by more than 51% through coordinated carbon reuse, and cuts carbon-trading expenditures by approximately 80%. Renewable energy is fully absorbed under adaptive coordination. Sensitivity analysis further indicates that higher carbon prices activate risk-aware responses that simultaneously reduce emissions and improve operating economics.