Research on Fuzzy Computation Tree Temporal Logic with Quality Constraints and Its Model Checking

This treatise represents a significant contribution to the field by integrating quality constraint functions and predicates into Possibility Computation Tree Temporal Logic (PoCTL), thus giving rise to Fuzzy Computation Tree Temporal Logic with Quality Constraints (QFCTL). We provide a comprehensive definition of QFCTL's syntax, conduct an in-depth analysis of its logical characteristics, outline a precise model checking algorithm for QFCTL, and perform a meticulous complexity assessment of said algorithm. Moreover, by enriching QFCTL with a quantitative characteristic predicate operator, we innovate, culminating in the development of an enhanced Fuzzy Computation Tree Temporal Logic with Quality Constraints (QFCTL*). The treatise explores the logical facets of QFCTL*, formulates a bespoke model checking algorithm for QFCTL*, and conducts a rigorous analysis of its algorithmic complexity. To attest to the practical utility and robust expressive power of QFCTL and QFCTL*, we present a model checking example that serves as empirical evidence of the efficacy of the proposed model checking algorithms.