Uniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as “covers”) in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by Gulwani and Musuvathi, and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution.

自 90 年代以来，一致插值在非经典命题逻辑中得到了大量研究。自动推理界的一个连续研究线调查了一阶理论中统一的无量词插值（有时称为“覆盖”）。这条进一步的研究路线的动机是均匀插值提供了一种有效的解决方案来解决量词消除和符号消除问题，这些问题是模型检查无限状态系统的核心。Gulwani 和 Musuvathi 在 2008 年的 ESOP 中首先指出了这一点，然后是当前贡献的作者在最近应用于验证数据感知过程的背景下指出的。在本文中，我们展示了封面如何与模型完成（模型理论中的一个众所周知的主题）严格相关。我们还通过采用微积分的约束版本并定义适当的设置和减少策略来研究叠加微积分中的覆盖计算。此外，我们表明，在处理数据感知过程的验证时，计算覆盖对于所使用的语言片段在计算上是易于处理的。通过分析使用以下方法获得的初步结果证实了这一观察结果mcmt工具来验证数据感知过程的相关示例。这些示例可以在工具分发的最新版本中找到。