A fuzzy real-time temporal logic

Abstract

High-level descriptions of real-time systems often use fuzzy notions of time that are left open to domain specific interpretations. In order to verify that a given implementation conforms to such loosely defined specifications, the typical approach is to verify the implementation to be correct within well defined limits of time tolerance. This approach determines whether the real-time requirements are met, but does not reflect how well it is met. Our goal in this paper is to prescribe the development of timed specifications using fuzzy notions of time, and to present a methodology for computing the quality of satisfaction of the specification on a given implementation using domain specific fuzzy membership functions. With this objective, we combine the notions of real-time interval temporal logic (like Metric Interval Temporal Logic) and fuzzy logic to derive FRTL, a fuzzy real-time temporal logic. The novelty of the proposed logic is in introducing the notion of fuzzy time intervals into the core fabric of conventional metric temporal logic. We present a method for evaluating the fuzzy truth of FRTL properties on finite traces. We discuss the motivation of computing the fuzzy truth towards evaluating the quality of control in time critical embedded control system applications. We also show that two important related problems from the domain of mixed-signal design verification, are subsumed by the proposed framework of analysis.