Derivation-Graph-Based Characterizations of Decidable Existential Rule Sets

Tim S. Lyon, Sebastian Rudolph

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 (\(\textbf{gbts}\)) and a new, generalized variant, called weakly gbts (\(\textbf{wgbts}\)). Revisiting and building on the notion of derivation graphs, we define (weakly) cycle-free derivation graph sets (\(\mathbf {(w)cdgs}\)) and employ elaborate proof-theoretic arguments to obtain that \(\textbf{gbts}\) and \(\textbf{cdgs}\) coincide, as do \(\textbf{wgbts}\) and \(\textbf{wcdgs}\). These novel characterizations advance our analytic proof-theoretic understanding of existential rules and will likely be instrumental in practice.