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First-order linear real arithmetic enriched with uninterpreted predicatesymbols yields an interesting modeling language. However, satisfiability ofsuch formulas is undecidable, even if we restrict the uninterpreted predicatesymbols to arity one. In order to find decidable fragments of this language, itis necessary to restrict the expressiveness of the arithmetic part. Onepossible path is to confine arithmetic expressions to difference constraints ofthe form $x - y \mathrel{\#} c$, where $\#$ ranges over the standard relations$<, \leq, =, \neq, \geq, >$ and $x,y$ are universally quantified. However, itis known that combining difference constraints with uninterpreted predicatesymbols yields an undecidable satisfiability problem again. In this paper, itis shown that satisfiability becomes decidable if we in addition bound theranges of universally quantified variables. As bounded intervals over the realsstill comprise infinitely many values, a trivial instantiation procedure is notsufficient to solve the problem.

The Bernays-Sch\"onfinkel-Ramsey Fragment with Bounded Difference Constraints over the Reals is Decidable