This talk by Terry Halpin and Matt Curland provides a brief overview of their Augmented Relational Calculus (ARC) language which is a version of first-order, 2-valued, domain relational calculus extended to support null items, aggregate functions and bags.
ARC provides a formal basis for expressing queries and derivation rules over Object-Role models. For non-technical users, ARC queries may be rephrased in a simpler syntax such as FORML.