近似函数依赖——重访蕴含问题
Approximate Functional Dependencies---Implication Problem Revisited
AI总结：
本文重访近似函数依赖的蕴含问题，指出其原子相互作用更复杂，证明Väänänen公理化在一元依赖下完备，还确定了其模型检测的复杂性。
AI中文摘要：
函数依赖是一类重要且被广泛研究的数据库约束，对应团队逻辑中依赖原子表达的概念。实际中数据常含错误，因此允许数据库存在少量违反期望依赖的元组有时是有用的。Väänänen（2017）研究了近似依赖概念的公理化，该概念为每个依赖原子指定可忽略的数据库比例。本文表明，近似依赖原子的相互作用比此前认为的更复杂，存在语义后承未被之前引入的推理规则捕获。本文还证明，Väänänen的公理化在一元依赖的受限情形下仍是完备的；同时研究了近似依赖的模型检测复杂性：两个原子的析取对应问题为NP-完全，单个原子则为LOGSPACE-难。
英文摘要：
Functional dependencies are an important and well-studied class of database constraints that correspond to a notion expressed by dependence atoms in team logic. In practice, data often contain errors, so in some cases it might be useful to allow the database to have a small number of tuples that violate the desired dependency. Väänänen (2017) studied the axiomatisation of a notion of approximate dependence that specifies for each dependence atom how much of the database can be disregarded. We demonstrate that the interaction of approximate dependence atoms is more complicated than previously thought in the sense that there is a semantic consequence that is not captured by the inference rules introduced before. We show that Väänänen's axiomatisation is still complete in the restricted case of unary dependencies. We also consider the complexity of model checking for approximate dependence: it is NP-complete for disjunctions of two atoms and LOGSPACE-hard for individual atoms.
