Computation tree logic model checking based on multi-valued possibility measures

Abstract

Multi-valued model checking has been studied extensively recently, but important uncertain information contained in systems of multi-valued logics has not been considered in previous work and, as a consequence, some serious deficiencies arise. To make up for these deficiencies, this paper considers the possibility information implied in multi-valued systems. Precisely, we investigate computation tree logic model checking based on multi-valued possibility measures. We model multi-valued logic systems by multi-valued Kripke structures (MvKSs) and specify their verification properties by multi-valued computation tree logic (MvCTL) formulae. Based on generalized possibility measures and generalized necessity measures, an MvCTL model checking method is proposed, the pseudocode of the corresponding model checking algorithm is presented, and its time complexity is analyzed in detail. Furthermore, after detailed comparisons with χCTL (introduced in Chechik et al. [10]) and the classical CTL, we show that MvCTL is more general than χCTL, but cannot be reduced to the classical CTL. The conditions on lattice and MvKS under which MvCTL is equivalent to χCTL are given. Finally, some examples and a case study are given to illustrate the MvCTL model-checking method.