Some multi-agent scenarios call for the possibility of evaluating specifications in a richer domain of truth values.Examples include runtime monitoring of a temporal property over a growing prefix of an infinite path, inconsistency analysis in distributed databases, and verification methods that use incomplete anytime algorithms, such as bounded model checking. In this paper, we present multi-valued ATL* (mv-ATLo), an expressive logic to specify strategic abilities in multi-agent systems.We show that our general method for model-independent translation from multi-valued to two-valued model checking cannot be directly extended to ATLo*. We also propose two ways of overcoming the problem. Firstly, we identify constraints on ATLo* formulas for which the model-independent translation can be suitably adapted. Secondly, we present a model-dependent reduction that can be applied to all formulas of ATLo*. We show that, in all cases, the complexity of verification increases only polynomially when new truth values are added to the evaluation domain. We also consider several examples that show possible applications of mv-ATLo and motivate its use for model checking MAS.

中文翻译：

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战略能力多值验证

一些多代理场景要求在更丰富的真值域中评估规范的可能性。示例包括对无限路径的不断增长的前缀上的时间属性的运行时监控、分布式数据库中的不一致分析以及随时使用不完整的验证方法算法，例如有界模型检查。在本文中，我们提出了多值 ATL* (mv-ATLo)，这是一种在多智能体系统中指定战略能力的表达逻辑。检查不能直接扩展到 ATLo*。我们还提出了两种克服问题的方法。首先，我们确定了 ATLo* 公式的约束，可以适当地调整与模型无关的翻译。第二，我们提出了一种依赖于模型的归约，它可以应用于 ATLo* 的所有公式。我们表明，在所有情况下，当新的真值被添加到评估域时，验证的复杂性只会以多项式的方式增加。我们还考虑了几个示例，这些示例展示了 mv-ATLo 的可能应用，并激发了其用于模型检查 MAS 的用途。