AI 中文总结
本文针对带例外的分层Datalog，研究其因果解释相关问题，证明了极小支撑集等无法确定因果性，刻画了最小意外情况规模，明确了相关问题的数据复杂度。
AI 中文摘要
带例外的基于规则推理需要能解释存在事实与不存在事实的因果解释。对于正Datalog，单调性允许极小支撑集确定删除因果性。分层否定消除了该属性，因为插入或删除一个事实可能产生或消除一个答案。我们在完美模型语义及有限可变外延事实集干预下，研究安全分层Datalog的实际原因、责任度与鲁棒性。我们证明极小支撑集及包含极小结果改变干预无法确定因果性，而鲁棒半径为1可能与无界最小意外情况共存。主要结果是通过观测结果与对立结果的兼容素蕴含项刻画候选事实的最小意外情况规模，该刻画保守恢复正Datalog的基于支撑集的因果性，并为受阻递归可达性生成路径-割刻画。对于固定非递归分层程序，我们确定原因识别、鲁棒性及责任度的数据复杂度为NP完全，且两类此类程序间的干预-响应等价性的数据复杂度为coNP完全。
英文摘要
Rule-based reasoning with exceptions requires causal explanations that account for both present and absent facts. For positive Datalog, monotonicity allows minimal supports to determine deletion causality. Stratified negation removes that property because inserting or deleting a fact may create or destroy an answer. We study actual causes, responsibility, and robustness for safe and stratified Datalog under perfect-model semantics and interventions over a finite set of mutable extensional facts. We prove that minimal supports and inclusion-minimal outcome-changing interventions do not determine causality, while robustness radius one may coexist with unbounded minimum contingencies. Our main result characterizes the minimum contingency size of a candidate fact by compatible prime implicants for the observed and opposite outcomes. The characterization conservatively recovers support-based causality for positive Datalog and yields path--cut characterizations for blocked recursive reachability. For fixed nonrecursive stratified programs, we establish data-complexity NP-completeness for cause recognition, robustness, and responsibility, and coNP-completeness for intervention-response equivalence between two such programs.
