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.

研究了带有分层否定的限制程序的扩展，发现它的附加表达能力使推理的计算需求更高，并提供了严格的数据复杂度界限。同时识别出一个具有可操作数据复杂度和足够表达能力以捕捉许多相关任务的片段。

限制 Datalog 程序中的分层否定