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We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form 
$\operatorname {\mathrm {Lsc}} (X,\overline {\mathbb {N}})$ for some 
$T_1$-space X. In our investigations, we also uncover new properties that the Cuntz semigroup of all AI-algebras satisfies.
