Motivated by applications in declarative data analysis, we study DatalogZ-an extension of Datalog with stratified negation and arithmetics over integers. Reasoning in this language is undecidable, so we present a fragment, called limit DatalogZ, that is powerful enough to naturally capture many important data analysis tasks. In limit DatalogZ, all intensional predicates with a numeric argument are limit predicates that keep only the maximal or minimal bounds on numeric values. Reasoning in limit DatalogZ is decidable if multiplication is used in a way that satisfies our linearity condition. Moreover, fact entailment in limit-linear DatalogZ is ΔEXP 2 -complete in combined and ΔP2 -complete in data complexity, and it drops to coNEXP and coNP, respectively, if only (semi-)positive programs are considered. We also propose an additional stability requirement, for which the complexity drops to EXP and P, matching the bounds for usual Datalog. Limit DatalogZ thus provides us with a unified logical framework for declarative data analysis and can be used as a basis for understanding the expressive power of the key data analysis constructs.

中文翻译：

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限制数据记录

受声明性数据分析应用的启发，我们研究了 DatalogZ——Datalog 的扩展，具有分层否定和整数上的算术。这种语言的推理是不可判定的，所以我们提出了一个片段，称为 limit DatalogZ，它足够强大，可以自然地捕获许多重要的数据分析任务。在 limit DatalogZ 中，所有带有数字参数的内涵谓词都是限制谓词，仅保留数值的最大或最小界限。如果以满足我们线性条件的方式使用乘法，则可以确定限制 DatalogZ 的推理。此外，极限线性 DatalogZ 中的事实蕴涵是 ΔEXP 2 -完全组合和 ΔP2 -完全数据复杂性，如果仅考虑（半）正程序，则它分别下降到 coNEXP 和 coNP。我们还提出了一个额外的稳定性要求，其复杂性下降到 EXP 和 P，与通常的 Datalog 的界限相匹配。因此，Limit DatalogZ 为我们提供了一个用于声明性数据分析的统一逻辑框架，并且可以作为理解关键数据分析结构的表达能力的基础。