Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency scheme as a mapping from QBF into DQBF. Our approach offers a fresh insight on the nature of soundness in proof systems for QBF with dependency schemes, in which a natural property called ‘full exhibition’ is central. We apply our approach to QBF proof systems from two distinct paradigms, termed ‘universal reduction’ and ‘universal expansion’. We show that full exhibition is sufficient (but not necessary) for soundness in universal reduction systems for QBF with dependency schemes, whereas for expansion systems the same property characterises soundness exactly. We prove our results by investigating DQBF proof systems, and then employing our reinterpretation of dependency schemes. Finally, we show that the reflexive resolution path dependency scheme is fully exhibited, thereby proving a conjecture of Slivovsky.

中文翻译：

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重新解释依赖方案：DQBF 中的健全性与不完备性

依赖量化布尔公式 (DQBF) 和 QBF 依赖方案已在文献中分开处理，尽管这两种处理都通过用偏序替换量词前缀的线性顺序来扩展 QBF。我们建议通过将依赖方案重新解释为从 QBF 到 DQBF 的映射来合并两者。我们的方法为具有依赖方案的 QBF 证明系统的可靠性提供了新的见解，其中称为“完整展示”的自然属性是核心。我们将我们的方法应用于来自两个不同范式的 QBF 证明系统，称为“通用归约”和“通用扩展”。我们表明，对于具有依赖方案的 QBF 的通用归约系统的健全性，充分展示是足够的（但不是必要的），而对于扩展系统，相同的属性准确地表征了健全性。我们通过研究 DQBF 证明系统来证明我们的结果，然后采用我们对依赖方案的重新解释。最后，我们证明了自反解析路径依赖方案得到了充分展示，从而证明了 Slivovsky 的猜想。