Model Checking with Multi-valued Logics

Bruns, Glenn; Godefroid, Patrice

doi:10.1007/978-3-540-27836-8_26

Cited by 59 publications

(65 citation statements)

References 16 publications

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“…As explained in [4,5], a Kripke structure (KS) can be extended to the multi-valued setting by assigning to each proposition in each state one of many (truth) values and likewise to each transition also a value, resulting in the notion of a multi-valued Kripke structure (mv-KS). A value of some proposition might then be interpreted as to which extend a proposition holds, a person may be trusted initially, or in which products of a product line a certain proposition holds.…”

Section: Introductionmentioning

confidence: 99%

“…Then, the semantics of a formula with respect to a mv-KS is one element of the lattice, denoting either the extent to which the formula holds, the trust value of some person performing actions, or the set of all products satisfying the formula. Model Checking multi-valued versions of the classical logics LTL, CTL, CTL * , and the μ-calculus has the been extensively studied already, for example in [6,4,5,7].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, it is important to study abstraction techniques also for multi-valued model checking. This paper studies abstraction and refinement techniques in the setting of multi-valued model checking for the μ-calculus as introduced in [5].…”

Section: Introductionmentioning

confidence: 99%

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Don’t Know for Multi-valued Systems

Campetelli

Gruler

Leucker

et al. 2009

Automated Technology for Verification and Analysis

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Abstract. This paper studies abstraction and refinement techniques in the setting of multi-valued model checking for the μ-calculus. Two dimensions of abstractions are identified and studied: Abstraction by joining states of the underlying multi-valued Kripke structure as well as abstraction of truth values, for each following both an optimistic and pessimistic account. It is shown that our notion of abstraction is conservative in the following sense: The truth value in a concrete system is "between" the optimistic and pessimistic assessment. Moreover, model checking of abstracted systems is shown to be again a multi-valued model checking problem, allowing to reuse multi-valued model checking engines. Finally, whenever the optimistic and pessimistic model checking result differ, the cause for such an assessment is identified, allowing the abstraction to be refined to eventually yield a result for which both the optimistic and pessimistic assessment coincide.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Don’t Know for Multi-valued Systems

Campetelli

Gruler

Leucker

et al. 2009

Automated Technology for Verification and Analysis

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“…Designing efficient algorithms for checking the satisfaction of 3-valued PAL formulae on KLMTSs, based on the definition above, is an interesting topic in itself and we leave it as further work. We now only note that, looking at similar results in the literature [3], it is to expect that such a model checking algorithm will not be more complex than the ones for checking (2-valued) PAL on KMs or LTSs.…”

Section: Semanticsmentioning

confidence: 68%

“…A standard Kripke model consists of a set of states S, the labelled relations R among them and a 2-valued valuation V which assigns a truth value to each basic proposition in each state 3 . In order to define abstractions of Kripke models the standard definition is extended in the following sense:…”

Section: Kripke Modal Labelled Transition Systemmentioning

confidence: 99%

Refinement of Kripke Models for Dynamics

Dechesne

Orzan

Wang

Theoretical Aspects of Computing - ICTAC 2008

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Abstract. We propose a property-preserving refinement/abstraction theory for Kripke Modal Labelled Transition Systems incorporating not only state mapping but also label and proposition lumping, in order to have a compact but informative abstraction. We develop a 3-valued version of Public Announcement Logic (PAL) which has a dynamic operator that changes the model in the spirit of public broadcasting. We prove that the refinement relation on static models assures us to safely reason about any dynamic properties in terms of PAL-formulas on the abstraction of a model. The theory is in particular interesting and applicable for an epistemic setting as the example of the Muddy Children puzzle shows, especially in the view of the growing interest for epistemic modelling and (automatic) verification of communication protocols.

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Abstraction for Falsification

Ball

Kupferman

Yorsh

2005

Computer Aided Verification

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Abstract. Abstraction is traditionally used in the process of verification. There, an abstraction of a concrete system is sound if properties of the abstract system also hold in the concrete system. Specifically, if an abstract state a satisfies a property ψ then all the concrete states that correspond to a satisfy ψ too. Since the ideal goal of proving a system correct involves many obstacles, the primary use of formal methods nowadays is falsification. There, as in testing, the goal is to detect errors, rather than to prove correctness. In the falsification setting, we can say that an abstraction is sound if errors of the abstract system exist also in the concrete system. Specifically, if an abstract state a violates a property ψ, then there exists a concrete state that corresponds to a and violates ψ too. An abstraction that is sound for falsification need not be sound for verification. This suggests that existing frameworks for abstraction for verification may be too restrictive when used for falsification, and that a new framework is needed in order to take advantage of the weaker definition of soundness in the falsification setting. We present such a framework, show that it is indeed stronger (than other abstraction frameworks designed for verification), demonstrate that it can be made even stronger by parameterizing its transitions by predicates, and describe how it can be used for falsification of branching-time and linear-time temporal properties, as well as for generating testing goals for a concrete system by reasoning about its abstraction.

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Model Checking with Multi-valued Logics

Cited by 59 publications

References 16 publications

Don’t Know for Multi-valued Systems

Don’t Know for Multi-valued Systems

Refinement of Kripke Models for Dynamics

Abstraction for Falsification

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