Model-Checking of Linear-Time Properties in Multi-Valued Systems

In this paper, we study model-checking of linear-time properties in multi-valuedsystems. Safety property, invariant property, liveness property, persistence anddual-persistence properties in multi-valued logic systems are introduced. Somealgorithms 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 thelaw 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 linear-time properties introducedin this paper have the new forms compared to those in classical logic. Com-pared to those classical model checking methods, our methods to multi-valuedmodel checking are more directly accordingly. A new form of multi-valued modelchecking with membership degree is also introduced. In particular, we show thatmulti-valued model-checking can be reduced to the classical model checking. Therelated verification algorithms are also presented. Some illustrative examples andcase study are also provided.