Foundations of Declarative Data Analysis Using Limit Datalog Programs
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Motivated by applications in declarative data analysis, we study Datalog_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 Datalog_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 requirement causes the complexity to drop to ExpTime and PTime, respectively. Finally, we show that stable Datalog_Z can express many useful data analysis tasks, and so our results provide a sound foundation for the development of advanced information systems.
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