Model checking of linear-time properties in multi-valued systems

Abstract

In this paper, we study the model-checking problem of linear-time properties in multi-valued systems. Safety properties, invariant properties, liveness properties, persistence and dual-persistence properties in multi-valued logic systems are introduced. Some algorithms related to the above multi-valued linear-time properties are discussed. The verification of multi-valued regular safety properties and multi-valued ω-regular properties using lattice-valued automata are thoroughly studied. Since the law of non-contradiction (i.e., a ∧ ¬a = 0) and the law of excluded-middle (i.e., a ∨ ¬a = 1) do not hold in multi-valued logic, the lineartime properties introduced in this paper have new forms compared to those in classical logic. Compared to those classical model-checking methods, our methods to multi-valued model checking are accordingly more direct: We give an algorithm for showing TS | = P for a model TS and a linear-time property P, which proceeds by directly checking the inclusion Traces(TS) ⊆ P instead of Traces(TS) ∩ ¬P = ∅. A new form of multi-valued model checking with membership degree is also introduced. In particular, we show that multi-valued model checking can be reduced to classical model checking. The related verification algorithms are also presented. Some illustrative examples and a case study are also provided.

Quantitative Safety and Liveness

“…We are not the first to define quantitative (or multi-valued) definitions of safety and liveness [41,27]. While the previously proposed quantitative generalizations of safety share strong similarities with our definition (without coinciding completely), our quantitative generalization of liveness is entirely new.…”

The μ-Calculus Model-Checking Algorithm for Generalized Possibilistic Decision Process

“…Hence, f 1 is monotonic, and f 2 is also monotonic, since f 1 , f 2 is monotonic, and the possibility value (0,1) is a finite complete lattice. According to Knaster-Tarski's theorem [11], f 1 , f 2 have a least fixpoint and greatest fixpoint, respectively. Similiar to the classical µ-calculus, the CTL formulae for the generalized possibilistic decision process can also be expressed by the GPo µ formulae.…”

“…Sci. 2020, 10, 2594 2 of 15 have proposed quantitative extensions to classical model checking, such as models that embed features into probability [5,6], possibility [7][8][9], and multi-valued [10][11][12], etc.Different model-checking approaches are applicable to different model types. Narasimha et al[13] proposed a model-checking algorithm based on the probabilistic labeled transition systems and µ-calculus to check whether the states in the finite probabilistic labeled transition systems satisfiy the logical formulas; Chechik et al [14] extended the classical CTL and Kripke structure and proposed a multi-valued model checking algorithm.…”

“…Sci. 2020, 10, 2594 2 of 15 have proposed quantitative extensions to classical model checking, such as models that embed features into probability [5,6], possibility [7][8][9], and multi-valued [10][11][12], etc.…”

Model Checking Fuzzy Computation Tree Logic Based on Fuzzy Decision Processes with Cost

“…Sometimes models may contain inconsistencies as they connect conflict points or contain components designed by different designers independently. In order to verify complex systems with inconsistencies and uncertainties, multi-valued model checking [ 9 , 10 , 11 , 12 ] is proposed. Fuzzy model checking [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ] pays more attention to the true value of the properties, which is another kind of uncertainty, caused by unclear concept extension [ 21 , 22 , 23 ].…”