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We propose a generic framework for establishing the decidability of a widerange of logical entailment problems (briefly called querying), based on theexistence of countermodels that are structurally simple, gauged by certaintypes of width measures (with treewidth and cliquewidth as popular examples).As an important special case of our framework, we identify logics exhibitingwidth-finite finitely universal model sets, warranting decidable entailment fora wide range of homomorphism-closed queries, subsuming a diverse set ofpractically relevant query languages. As a particularly powerful width measure,we propose Blumensath's partitionwidth, which subsumes various other commonlyconsidered width measures and exhibits highly favorable computational andstructural properties. Focusing on the formalism of existential rules as apopular showcase, we explain how finite partitionwidth sets of rules subsumeother known abstract decidable classes but - leveraging existing notions ofstratification - also cover a wide range of new rulesets. We expose naturallimitations for fitting the class of finite unification sets into our pictureand provide several options for remedy.

Decidability of Querying First-Order Theories via Countermodels of Finite Width