The Shapley value, originally introduced in cooperative game theory for wealth distribution, has found use in KR and databases for the purpose of assigning scores to formulas and database tuples based upon their contribution to obtaining a query result or inconsistency. In the present paper, we explore the use of Shapley values in ontology-mediated query answering (OMQA) and present a detailed complexity analysis of Shapley value computation (SVC) in the OMQA setting. In particular, we establish a PF/#P-hard dichotomy for SVC for ontology-mediated queries (T,q) composed of an ontology T formulated in the description logic ELHI_\bot and a connected constant-free homomorphism-closed query q. We further show that the #P-hardness side of the dichotomy can be strengthened to cover possibly disconnected queries with constants. Our results exploit recently discovered connections between SVC and probabilistic query evaluation and allow us to generalize existing results on probabilistic OMQA.

翻译：Shapley值最初在合作博弈论中引入用于财富分配，现已在知识表示与数据库领域得到应用，其作用是根据公式和数据库元组对获得查询结果或不一致性的贡献度进行评分。本文探讨了Shapley值在本体介导查询应答中的应用，并对OMQA场景下的Shapley值计算进行了详细的复杂性分析。特别地，我们针对由描述逻辑ELHI⊥形式化的本体T与连通无常量同态封闭查询q构成的本体介导查询(T,q)，建立了SVC的PF/#P-困难二分定理。进一步证明该二分定理的#P-困难侧可推广至包含常量且可能非连通的查询。我们的研究成果利用了近期发现的SVC与概率查询评估之间的关联，从而能够推广概率OMQA领域的现有结论。