递归数据日志中的因果关系和最小支持集
Causality and Minimal Supports in Recursive Datalog
AI总结：
研究递归数据日志中因果关系和最小支持集问题，通过基于删除的解释，将支持集组织成超图，证明其能确定多种因果关系等，区分非递归查询与递归数据日志，还给出正长度可达性相关结论及NP难校准。
AI中文摘要：
递归规则评估比非递归查询回答更难解释。对于合取查询的固定并集，每个解释都受查询主体限制。对于递归规则，相同答案可能依赖大支持集，且最小支持集数量可能呈指数级。我们通过基于删除的解释研究此差距，使用包含最小的内生输入事实以及固定背景事实来推导原子。我们将这些支持集组织成超图，并证明它能确定实际原因、反事实原因、责任和删除鲁棒性。此结果观点在最小输入解释层面区分了非递归查询和递归数据日志。对于正长度可达性，最小支持集恰好是简单有向路径，删除鲁棒性是最小有向边割。我们还证明了在固定目标等效正数据日志程序下的不变性以及鲁棒性阈值问题的NP难校准。
英文摘要：
Explaining an inferred fact under rule evaluation can require identifying the inclusion-minimal input sets that suffice for the inference and the deletions that make the fact disappear. For a fixed union of conjunctive queries, every minimal support is bounded by the query body. For recursive rules, the same answer may depend on large supports, and the number of minimal supports may be exponential in the input. We study the gap through deletion-based explanation, using inclusion-minimal endogenous input facts that entail the atom together with fixed background facts. We organize these supports as a hypergraph and prove that it determines actual causes, counterfactual causes, responsibility, and deletion robustness. The resulting view separates nonrecursive queries from recursive Datalog at the level of minimal input explanations. For positive-length reachability, minimal supports are exactly simple directed paths, and deletion robustness is the minimum directed edge cut. We also prove invariance under fixed-goal equivalent positive Datalog programs and an NP-hardness calibration for the robustness threshold problem.
