Derivation-Graph-Based Characterizations of Decidable Existential Rule Sets

TL;DR

This paper introduces new graph-based characterizations for classes of existential rule sets with decidable query entailment, enhancing theoretical understanding and potential practical applications.

Contribution

It presents novel derivation-graph characterizations for greedy bounded-treewidth sets and their variants, linking them to cycle-free derivation graph sets.

Findings

gbts and cdgs coincide

wgbts and wcdgs coincide

advances proof-theoretic understanding of existential rules

Abstract

This paper establishes alternative characterizations of very expressive classes of existential rule sets with decidable query entailment. We consider the notable class of greedy bounded-treewidth sets (gbts) and a new, generalized variant, called weakly gbts (wgbts). Revisiting and building on the notion of derivation graphs, we define (weakly) cycle-free derivation graph sets ((w)cdgs) and employ elaborate proof-theoretic arguments to obtain that gbts and cdgs coincide, as do wgbts and wcdgs. These novel characterizations advance our analytic proof-theoretic understanding of existential rules and will likely be instrumental in practice.