Stratified Negation in Limit Datalog Programs

TL;DR

This paper extends limit Datalog programs with stratified negation, analyzing the increased computational complexity and identifying a fragment with tractable data complexity suitable for many data analysis tasks.

Contribution

It introduces stratified negation into limit programs, providing complexity bounds and a tractable fragment for expressive data analysis.

Findings

Adding negation increases reasoning complexity

A tractable fragment with sufficient expressivity is identified

Complexity bounds for the extended language are established

Abstract

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.