This paper introduces the concept and the general theory of multi-valued model checking, and describes a multi-valued symbolic model-checker \Chi Chek. Multi-valued

Counter-examples explain why a desired temporal logic property fails to hold, and as such considered to be the most useful form of output from modelcheckers.

Abstract not found

Multi-valued model-checking is an effective technique for reasoning about systems with in-complete or inconsistent information. In particular, it is well suited for reasoning about ab-stract, partial, and feature-based system descriptions. The technique is based on extending the classical model-checking algorithm over two-valued logic to arbitrary finite logics whose truth values form a distributive De Morgan lattice. In this thesis we address several issues surrounding the usability of multi-valued model-checking. Firstly, we provide an improved analysis of the worst-case complexity of the sym-bolic multi-valued model-checking algorithm, and show that it is independent of the height of the lattice. Secondly, we extend the notion of fairness to a multi-valued models, thus enabling application of multi-valued model-checking to asynchronous concurrent systems. Thirdly, we introduce multi-valued witnesses and counter-examples that aid in interpreting the results of the model-checker. Finally, we describe the design and implementation of a multi-valued model-checker χChek.

In earlier work [9], we defined CTL model-checking over finite-valued logics with De Morgan negation. In this paper, we extend this work to logics with intuitionistic, Galois and minimal negations, calling the resulting language CTL. We define CTL operators and show that they can be computed using fixpoints. We further discuss how to extend our existing multi-valued model-checker Chek [8] to reasoning over these logics.

Abstract. This work extends the game-based framework of µ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. We define a new game for this problem and derive from it a direct model checking algorithm that handles the multi-valued structure without any reduction. We investigate the properties of the new game, both independently, and in comparison to the automata-based approach. We show that the usual resemblance between the two approaches does not hold in the multivalued setting and show how it can be regained by changing the nature of the game. 1

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William Chan [3] 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.

This paper develops a framework for solving temporal-logic query-checking problems for a class of infinite-state system models that compute with integer-valued variables (so-called Presburger systems, in which Presburger formulas are used to define system behavior). The temporal-logic query-checking problem may be formulated as follows: given a model and a temporal logic formula with placeholders, compute a set of assignments of formulas to placeholders such that the resulting temporal formula is satisfied by the given model. Temporal-logic query checking has proved useful as a means for requirements and design understanding; existing work, however, has focused only on propositional temporal logic and finite-state systems. Our method is based on a symbolic model-checking technique that relies on proof search. The paper first introduces this model-checking approach and then shows how it can be adapted to solving the temporal queries in which formulas may contain integer variables. We also present experimental results showing the computational efficacy of our approach.

... ΧChek. Multi-valued model-checking generalizes classical model-checking and is useful for analyzing models where there is uncertainty (e.g. missing information) or inconsistency (e.g. disagreement between different views). Multi-valued logics support the explicit modeling of uncertainty and disagreement by providing additional truth values in the logic. ΧChek 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 # CTL, our multi-valued extension of the temporal logic CTL. This paper gives a brief summary of the model checker and describes some applications.