Turning decision procedures into disprovers

A class of many‐sorted polyadic set algebras is introduced. These generalise structure and model in a way that is relevant in regards to the Entscheidungsproblem and to automated reasoning. A downward Löwenheim‐Skolem property is shown in that each satisfiable finite conjunction of purely relational first‐order prenex sentences has a finite generalised model. This property does, together with a construction related to doubling the size of a finite structure, provide several strict generalisations of the strategy of finite model search for disproving. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)