Foundations of Declarative Data Analysis Using Limit Datalog Programs


Motivated by applications in declarative data analysis, we study DatalogZ\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 limit DatalogZ\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 stability\mathit{stability} requirement causes the complexity to drop to ExpTime and PTime, respectively. Finally, we show that stable DatalogZ\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.Comment: 23 pages; full version of a paper accepted at IJCAI-17; v2 fixes some typos and improves the acknowledgment

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