The Shapley value, originating from cooperative game theory, has been employed to define responsibility measures that quantify the contributions of database facts to obtaining a given query answer. For non-numeric queries, this is done by considering a cooperative game whose players are the facts and whose wealth function assigns 1 or 0 to each subset of the database, depending on whether the query answer holds in the given subset. While conceptually simple, this approach suffers from a notable drawback: the problem of computing such Shapley values is #P-hard in data complexity, even for simple conjunctive queries. This motivates us to revisit the question of what constitutes a reasonable responsibility measure and to introduce a new family of responsibility measures -- weighted sums of minimal supports (WSMS) -- which satisfy intuitive properties. Interestingly, while the definition of WSMSs is simple and bears no obvious resemblance to the Shapley value formula, we prove that every WSMS measure can be equivalently seen as the Shapley value of a suitably defined cooperative game. Moreover, WSMS measures enjoy tractable data complexity for a large class of queries, including all unions of conjunctive queries. We further explore the combined complexity of WSMS computation and establish (in)tractability results for various subclasses of conjunctive queries.

翻译：沙普利值源于合作博弈论，已被用于定义责任度量，以量化数据库事实对获得特定查询答案的贡献。对于非数值查询，该方法通过构造一个合作博弈来实现：博弈参与者为数据库事实，财富函数根据查询答案在给定子集中是否成立，为每个数据库子集分配1或0。尽管概念简单，该方法存在显著缺陷：即使对于简单合取查询，计算此类沙普利值在数据复杂度上也是#P-难的。这促使我们重新审视合理责任度量的构成标准，并引入新的责任度量族——最小支持集的加权和（WSMS）——其满足直观的性质。有趣的是，虽然WSMS的定义简单且与沙普利值公式无明显相似性，我们证明每个WSMS度量均可等价视为特定合作博弈的沙普利值。此外，对于包括所有合取查询并集在内的大类查询，WSMS度量具有可处理的数据复杂度。我们进一步探究WSMS计算的组合复杂度，并为合取查询的多个子类建立了（不）可处理性结果。