  We prove a version of uniqueness theorem for Cuntz-Pimsner algebras of
discrete product systems over semigroups of Ore type. To this end, we introduce
Doplicher-Roberts picture of Cuntz-Pimsner algebras, and the semigroup dual to
a product system of 'regular' C*-correspondences. Under a certain aperiodicity
condition on the latter, we obtain the uniqueness theorem and a simplicity
criterion for the algebras in question. These results generalize the
corresponding ones for crossed products by discrete groups, due to Archbold and
Spielberg, and for Exel's crossed products, due to Exel and Vershik. They also
give interesting conditions for topological higher rank graphs and $P$-graphs,
and apply to the new Cuntz C*-algebra $\mathcal{Q}_\mathbb{N}$ arising from the
"$ax+b$"-semigroup over $\mathbb{N}$.
