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

Derivation-Graph-Based Characterizations of Decidable Existential Rule Sets