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Stratified Negation in Limit Datalog Programs
There has recently been an increasing interest in declarative data analysis,
where analytic tasks are specified using a logical language, and their
implementation and optimisation are delegated to a general-purpose query
engine. Existing declarative languages for data analysis can be formalised as
variants of logic programming equipped with arithmetic function symbols and/or
aggregation, and are typically undecidable. In prior work, the language of
was proposed, which is sufficiently powerful to
capture many analysis tasks and has decidable entailment problem. Rules in this
language, however, do not allow for negation. In this paper, we study an
extension of limit programs with stratified negation-as-failure. We show that
the additional expressive power makes reasoning computationally more demanding,
and provide tight data complexity bounds. We also identify a fragment with
tractable data complexity and sufficient expressivity to capture many relevant
tasks.Comment: 14 pages; full version of a paper accepted at IJCAI-1
Foundations of Declarative Data Analysis Using Limit Datalog Programs
Motivated by applications in declarative data analysis, we study
---an extension of positive Datalog with
arithmetic functions over integers. This language is known to be undecidable,
so we propose two fragments. In
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
requirement causes the complexity to drop to ExpTime and PTime, respectively.
Finally, we show that stable 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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