This paper proposes a semantics ABS for the model-theoretic interpretation of annotation structures. It provides a language ABSr, that represents semantic forms in a (possibly 𝜆-free) type-theoretic first-order logic. For semantic compositionality, the representation language introduces two operators ⊕ and ⊘ with subtypes for the conjunctive or distributive composition of semantic forms. ABS also introduces a small set of logical predicates to represent semantic forms in a simplified format. The use of ABSr is illustrated with some annotation structures that conform to ISO 24617 standards on semantic annotation such as ISO-TimeML and ISO-Space.