Abstract The purpose of this paper is twofold. First, it proposes a compositional semantic analysis for approximative kaada in Classical Arabic which has the property of being a clause-level rather than predicate-level operator: [KAADA α] is paraphrased as [α is false but there exists β close to α such that β is true]. The analysis is based on the integrated semantics of Penka (Penka, Doris. 2006. Almost there: The meaning of almost. Proceedings of Sinn und Bedeutung 10. 275–286) in which the negativity component of kaada is interpreted as part of its lexical meaning within a situation semantics framework. It also makes a novel use of the concept of semantic closeness among situations in terms of the intuitively appealing dimension of the relative completion of an event. Second, the paper presents and analyzes an instance of a puzzle noted by most descriptive Classical Arabic grammarians (see, for example, al-Ahmad, Ayman. 2021. Dalalit KAADA l-manfiah fi l-Qurʾaan l-kareem. Journal of the Association of Arab Universities for Literature 9(2). 838–859) in which negated kaada has an interpretation where the negativity implication disappears altogether. The paper offers a solution to the puzzle based on a previous suggestion made by Kilbourn-Ceron (Kilbourn-Ceron, Oriana. 2016. Embedded exhaustification: Evidence from almost. Journal of Semantics 34(1). 43–60) in which an instance of embedded exhaustification appears to apply in approximatives in certain contexts in such a way that the negativity inference is obscured.