To enhance the model checking procedure for handling more complex temporal logic specifications or larger state spaces, one could explore techniques such as parallelization to distribute the computational load across multiple processors or machines. This would help in speeding up the verification process for larger systems. Additionally, incorporating more sophisticated abstraction techniques or refinement strategies could improve the precision of the analysis, reducing the over-approximation errors and providing more accurate verification results. Furthermore, integrating machine learning algorithms for pattern recognition or anomaly detection could assist in handling complex temporal logic specifications by learning patterns from data and identifying violations more efficiently.