Motivated by applications in declarative data analysis, we study
$\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with
arithmetic functions over integers. This language is known to be undecidable,
so we propose two fragments. In $\mathit{limit}~\mathit{Datalog}_{\mathbb{Z}}$
predicates are axiomatised to keep minimal/maximal numeric values, allowing us
to show that fact entailment is coNExpTime-complete in combined, and
coNP-complete in data complexity. Moreover, an additional $\mathit{stability}$
requirement causes the complexity to drop to ExpTime and PTime, respectively.
Finally, we show that stable $\mathit{Datalog}_{\mathbb{Z}}$ can express many
useful data analysis tasks, and so our results provide a sound foundation for
the development of advanced information systems.

研究了正 Datalog 上添加整数算术函数的扩展语言 Datalog_Z，并提出了两个限制子语言 limit Datalog_Z 和 stable Datalog_Z 以解决其不可判定性，并证明了相应的 NP 完全性和 ExpTime 完全性，最终表明稳定的 Datalog_Z 能够表达许多有用的数据分析任务，为先进信息系统的发展提供了一个坚实的基础。