First-order linear rational arithmetic enriched with uninterpreted predicates yields an interesting and very expressive modeling language. However, already the presence of a single uninterpreted predicate symbol of arity one or greater renders the associated satisfiability problem undecidable. We identify two decidable fragments, both based on the Bernays–Schönfinkel–Ramsey prefix class. Due to the inherent infiniteness of the underlying domain, a finite model property in the usual sense cannot be established. Nevertheless, we show that satisfiable sentences always have a model that can be described by finite means. To this end, we restrict the syntax of arithmetic atoms. In the first fragment that is presented, arithmetic operations are only allowed over terms without universally quantified variables. In the second fragment, arithmetic atoms are essentially confined to difference constraints over universally quantified variables with bounded range. We will call such atoms bounded difference constraints. As bounded intervals over the rationals still comprise infinitely many values, a trivial instantiation procedure is not sufficient to solve the satisfiability problem. After a slight shift of perspective, the positive decidability result for the first fragment can be restated in the framework of combinations of theories over non-disjoint vocabularies. More precisely, we combine first-order theories that share a dense total order without endpoints.

富含未解释谓词的一阶线性有理算术产生了一种有趣且非常富表现力的建模语言。但是，已经存在单个未解释的谓词“一个或多个”的情况使得相关的可满足性问题无法确定。我们根据Bernays–Schönfinkel–Ramsey前缀类确定两个可确定的片段。由于基础领域的固有无限性，因此无法建立通常意义上的有限模型属性。但是，我们表明，可满足的句子始终具有可以用有限方式描述的模型。为此，我们限制了算术原子的语法。在显示的第一个片段中，只允许对没有通用量化变量的项进行算术运算。在第二个片段中 算术原子本质上被限制在有界范围的普遍量化变量的差异约束上。我们称这种原子有界差约束。由于有理区间上的有界区间仍然包含无限多个值，因此琐碎的实例化过程不足以解决可满足性问题。在稍微改变了观点之后，第一个片段的正可判定性结果可以在理论组合的基础上重述不相交词汇表。更准确地说，我们结合了具有密集总顺序而没有端点的一阶理论。