This article introduces the concept of multi-valued model-checking and describes a multi-valued symbolic model-checker, ΧChek. Multi-valued model-checking is a generalization of classical model-checking, useful for analyzing models that contain uncertainty (lack of essential information) or inconsistency (contradictory information, often occurring when information is gathered from multiple sources). Multi-valued logics support the explicit modeling of uncertainty and disagreement by providing additional truth values in the logic.This article provides a theoretical basis for multi-valued model-checking and discusses some of its applications. A companion article [Chechik et al. 2002b] describes implementation issues in detail. The model-checker works for any member of a large class of multi-valued logics. Our modeling language is based on a generalization of Kripke structures, where both atomic propositions and transitions between states may take any of the truth values of a given multi-valued logic. Properties are expressed in ΧCTL, our multi-valued extension of the temporal logic CTL.We define the class of logics, present the theory of multi-valued sets and multi-valued relations used in our model-checking algorithm, and define the multi-valued extensions of CTL and Kripke structures. We explore the relationship between ΧCTL and CTL, and provide a symbolic model-checking algorithm for ΧCTL. We also address the use of fairness in multi-valued model-checking. Finally, we discuss some applications of the multi-valued model-checking approach.
