The infinite-domain CSP dichotomy conjecture extends the finite-domain CSP dichotomy theorem to reducts of finitely bounded homogeneous structures. Every such structure is uniquely described by a particular sentence of the logic SNP. We show that the question whether a given SNP sentence describes a structure within the scope of the conjecture is undecidable even if the sentence comes from the connected Datalog fragment, and that the closely related problem of testing the amalgamation property for universal sentences is EXPSPACE-hard. We also discuss some philosophical implications of these results for the infinite-domain CSP dichotomy conjecture.

翻译：无限域CSP二分猜想将有限域CSP二分定理推广至有限有界齐次结构的约简。每个此类结构均可由逻辑SNP中的特定句子唯一描述。我们证明，即便给定句子源自连通Datalog片段，判定该句子是否描述猜想适用范围内结构的问题是不可判定的；同时，与通用句子融合性质检验密切相关的难题属于EXPSPACE-hard。本文还讨论了这些结果对无限域CSP二分猜想的若干哲学启示。