Motivated by applications in declarative data analysis, we study
DatalogZ​---an extension of positive Datalog with
arithmetic functions over integers. This language is known to be undecidable,
so we propose two fragments. In limit DatalogZ​
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 stability
requirement causes the complexity to drop to ExpTime and PTime, respectively.
Finally, we show that stable DatalogZ​ can express many
useful data analysis tasks, and so our results provide a sound foundation for
the development of advanced information systems.Comment: 23 pages; full version of a paper accepted at IJCAI-17; v2 fixes some
typos and improves the acknowledgment