Foundations of Declarative Data Analysis Using Limit Datalog Programs

Motivated by applications in declarative data analysis, we study mathitDatalog_mathbbZ---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two fragments. In mathitlimit~mathitDatalog_mathbbZ 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 mathitstability requirement causes the complexity to drop to ExpTime and PTime, respectively. Finally, we show that stable mathitDatalog_mathbbZ can express many useful data analysis tasks, and so our results provide a sound foundation for the development of advanced information systems.