Query Answering with Transitive and Linear-Ordered Data

TL;DR

This paper explores the decidability and complexity of entailment problems involving transitive, transitive closure, and linear order constraints within powerful guarded existential rule frameworks.

Contribution

It introduces generalized guardedness conditions that ensure decidability for these constraints and analyzes how minor modifications lead to undecidability.

Findings

Decidability is maintained under certain generalized guardedness conditions.

Complexity of decision problems is characterized for each constraint type.

Small changes in conditions cause undecidability.

Abstract

We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put 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 generalizations 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 our conditions lead to undecidability.