We consider the issue of answering unions of conjunctive queries (UCQs) with
disjunctive existential rules and mappings. While this issue has already been
well studied from a chase perspective, query rewriting within UCQs has hardly
been addressed yet. We first propose a sound and complete query rewriting
operator, which has the advantage of establishing a tight relationship between
a chase step and a rewriting step. The associated breadth-first query rewriting
algorithm outputs a minimal UCQ-rewriting when one exists. Second, we show that
for any ``truly disjunctive'' nonrecursive rule, there exists a conjunctive
query that has no UCQ-rewriting. It follows that the notion of finite
unification sets (fus), which denotes sets of existential rules such that any
UCQ admits a UCQ-rewriting, seems to have little relevance in this setting.
Finally, turning our attention to mappings, we show that the problem of
determining whether a UCQ admits a UCQ-rewriting through a disjunctive mapping
is undecidable. We conclude with a number of open problems.

本文研究了使用拼接查询组成的联合响应（UCQs）答案问题，有 “或型存在规则和映射”。本文首先提出了一个完整的查询重写操作符，并使用广度优先查询重写算法来输出最小的 UCQ 重写副本。其次，我们证明，在任何真正的 “分离” 递归规则中，存在一种联合查询，不需要 UCQ 重写。最后，本文研究了通过 “或型映射” 决定 UCQ 是否有 UCQ 重写的问题，结果是不可判定的。