Stratified Negation in Limit Datalog Programs
This work addresses the need for more expressive yet decidable logical languages in data analysis, though it is incremental as it builds on prior limit program frameworks.
The paper tackles the problem of extending limit Datalog programs with stratified negation to enhance expressivity for declarative data analysis, showing that this addition increases computational complexity but identifying a tractable fragment that still captures many tasks.
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 $\mathit{limit\ programs}$ 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.