Query Answering with Transitive and Linear-Ordered Data

Abstract

We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation to be transitive, restricting a relation to be the transitive closure of another relation, and restricting a relation to be a linear order. We give some natural variants of guardedness that allow inference to be decidable in each case, and isolate the complexity of the corresponding decision problems. Finally we show that slight changes in these conditions lead to undecidability.

This article was originally published at JAIR in 2018: https://www.jair.org/index.php/jair/article/view/11240 (DOI 10.1613/jair.1.11240). This version of the paper includes one modification from the publisher version: we fix an incorrect proof for one of our undecidability results (Theorem 6.2). arXiv admin note: substantial text overlap with arXiv:1607.00813