Abstraction and approximation in fuzzy temporal logics and models

Abstract

Recently, by defining suitable fuzzy temporal logics, temporal properties of dynamic systems are specified during model checking process, yet a few numbers of fuzzy temporal logics along with capable corresponding models are developed and used in system design phase, moreover in case of having a suitable model, it suffers from the lack of a capable model checking approach. Having to deal with uncertainty in model checking paradigm, this paper introduces a fuzzy Kripke model (FzKripke) and then provides a verification approach using a novel logic called Fuzzy Computation Tree Logic* (FzCTL*). Not only state space explosion is handled using well-known concepts like abstraction and bisimulation, but an approximation method is also devised as a novel technique to deal with this problem. Fuzzy program graph, a generalization of program graph and FzKripke, is also introduced in this paper in consideration of higher level abstraction in model construction. Eventually modeling, and verification of a multi-valued flip-flop is studied in order to demonstrate capabilities of the proposed models.

Symbolic checking of Fuzzy CTL on Fuzzy Program Graph

“…Fuzzy Kripke Model (FzKripke) Structure [26] is basically χ Kripke Model [6] whose quasiboolean algebra is defined on infinite lattice of interval [0,1]. Similarly the Quantized FzKripke (Q-FzKripke) can be defined over quantized [0,1].…”

“…Unfortunately, no one could devised an applicable model checking method for FBTL yet. If such an approach should happen to contrive then it will be based on a simpler fuzzy extended temporal logic defined in discrete time [26]. Therefore, in this paper, we are providing more comprehensive semantics in formal verification of discrete-time fuzzy systems.…”

“…Although fuzzy Markov chain is a good candidate to model discrete-time fuzzy logic systems, we simply believe this is a matter of preference. This paper neither aims nor intends to compare discrete-time fuzzy logic models but since semantics of our specification language is defined based on this structure [26] and we simply do not intend to reinvent the wheel, FzKripke structure is our choice of model for discrete-time fuzzy systems. FzKripke structure is capable of modeling fuzzy logic controllers, and fuzzy logic circuitry.…”

“…FzKripke structure is capable of modeling fuzzy logic controllers, and fuzzy logic circuitry. It was even used for modeling fuzzy flip-flops, and a medical diagnosis and treatment example [22,26].…”

“…Sotudeh also defined a higher-level abstraction of FzKripke structure that is more compact, and easier to manually manipulate called Fuzzy Program Graph (FzPG) [26]. Although FzPG is more efficient in modeling phase, its verification requires a direct translation to an equal FzKripke structure resulting in an exponential blow-up.…”