We consider the complexity of the open-world query answering problem, where we wish to determine certain answers to conjunctive queries over incomplete datasets specified by an initial set of facts and a set of guarded TGDs. This problem has been well-studied in the literature and is decidable but with a high complexity, namely, it is 2EXPTIME complete. Further, the complexity shrinks by one exponential when the arity is fixed. We show in this paper how we can obtain better complexity bounds when considering separately the arity of the guard atom and that of the additional atoms, called the side signature. Our results make use of the technique of linearizing guarded TGDs, introduced in Gottlob, Manna, and Pieris. Specifically, we present a variant of the linearization process, making use of a restricted version of the chase that we recently introduced. Our results imply that open-world query answering with guarded TGDs can be solved in EXPTIME with arbitrary-arity guard relations if we simply bound the arity of the side signature; and that the complexity drops to NP if we fix the side signature and bound the width of the dependencies.

翻译：我们考虑开放世界查询回答问题的复杂性，该问题旨在确定由初始事实集和带守卫TGD集指定的不完整数据集上的合取查询的确定性答案。该问题在文献中已被充分研究，虽可判定但复杂度极高，即为2EXPTIME完全。进一步，当元数固定时，复杂度会降低一个指数级。本文展示了如何通过分别考虑守卫原子的元数和附加原子的元数（称为侧签名），获得更好的复杂度界。我们的结果利用了Gottlob、Manna和Pieris引入的线性化带守卫TGD技术。具体而言，我们提出了一种线性化过程的变体，使用了我们近期引入的限制版追逐算法。结果表明，若仅限制侧签名的元数，则任意元数守卫关系下的开放世界查询回答可在EXPTIME内求解；若固定侧签名并限制依赖关系的宽度，则复杂度降至NP。