In this paper we define the first-order fragment of the Object Constraint Language (OCL), the declarative language for describing rules that apply to conceptual schemas in the Unified Modelling Language (UML). This fragment covers the whole of OCL without arithmetic operators, aggregation functions, iterators, and recursion. We give the set theoretical formal syntax and semantics in an elegant, concise, and clear way. This fragment has the same expressivity as domain-independent first-order logic (aka relational algebra), in the sense that any relational algebra expression can be reformulated as a logically equivalent OCL expression, and vice-versa.

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