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In our pursuit of generic criteria for decidable ontology-based querying, weintroduce 'finite-cliquewidth sets' (FCS) of existential rules, amodel-theoretically defined class of rule sets, inspired by the cliquewidthmeasure from graph theory. By a generic argument, we show that FCS ensuresdecidability of entailment for a sizable class of queries (dubbed 'DaMSOQs')subsuming conjunctive queries (CQs). The FCS class properly generalizes theclass of finite-expansion sets (FES), and for signatures of arity at most 2,the class of bounded-treewidth sets (BTS). For higher arities, BTS is onlyindirectly subsumed by FCS by means of reification. Despite the generality ofFCS, we provide a rule set with decidable CQ entailment (by virtue offirst-order-rewritability) that falls outside FCS, thus demonstrating theincomparability of FCS and the class of finite-unification sets (FUS). In spiteof this, we show that if we restrict ourselves to single-headed rule sets oversignatures of arity at most 2, then FCS subsumes FUS.

Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying