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 logical frameworks, identifying conditions for decidability and undecidability.

Contribution

It introduces natural variants of guardedness that ensure decidability for these constraints and analyzes their complexity, highlighting how slight modifications lead to undecidability.

Findings

Decidability is achieved under certain guardedness variants.

Complexity results are established for each case.

Minor changes in conditions cause undecidability.

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.