Program logics typically reason about an over-approximation of program behaviour to prove the absence of bugs. Recently, program logics have been proposed that instead prove the presence of bugs by means of under-approximate reasoning, which has the promise of better scalability. In this paper, we present an under-approximate program logic for a nondeterministic graph programming language, and show how it can be used to reason deductively about program incorrectness, whether defined by the presence of forbidden graph structure or by finitely failing executions. We prove this incorrectness logic to be sound and complete, and speculate on some possible future applications of it.

中文翻译：

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图程序的不正确逻辑

程序逻辑通常会通过过度逼近程序行为来证明不存在错误。近来，已经提出了程序逻辑，该程序逻辑通过欠近似推理来证明错误的存在，这有望带来更好的可伸缩性。在本文中，我们为一种不确定的图编程语言提供了一种近似的程序逻辑，并展示了如何用它来演绎性地推断程序的不正确性，无论是由禁止图形结构的存在还是由有限失败的执行所定义的。我们证明了这种错误逻辑是合理且完整的，并推测了它的某些未来应用。