This article introduces the concept of multi-valued model-checking and describes a multi-valued symbolic model-checker, χ Chek. Multi-valued model-checking is a generalization of classical modelchecking, 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 χ CTL, 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 χ CTL and CTL, and provide a symbolic modelchecking algorithm for χ CTL. We also address the use of fairness in multi-valued model-checking. Finally, we discuss some applications of the multi-valued model-checking approach.
Temporal logic query checking was first introduced by W. Chan in order to speed up design understanding by discovering properties not known a priori. A query is a temporal logic formula containing a special symbol ? 1 , known as a placeholder. Given a Kripke structure and a propositional formula ', we say that ' satisfies the query if replacing the placeholder by ' results in a temporal logic formula satisfied by the Kripke structure. A solution to a temporal logic query on a Kripke structure is the set of all propositional formulas that satisfy the query. Query checking helps discover temporal properties of a system and, as such, is a useful tool for model exploration. In this paper, we show that query checking is applicable to a variety of model exploration tasks, ranging from invariant computation to test case generation. We illustrate these using a Cruise Control System. Additionally, we show that query checking is an instance of a multi-valued model checking of Chechik et al. This approach enables us to build an implementation of a temporal logic query checker, TLQSolver, on top of our existing multi-valued model checker 1Chek. It also allows us to decide a large class of queries and introduce witnesses for temporal logic queries-an essential notion for effective model exploration.
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