This paper offers an exploratory Interactional Linguistic account of the role that inferences play in episodes of ordinary conversational interaction. To this end, it systematically reconsiders the conversational practice of using the lexico-syntactic format oh that’s right to implicitly claim “just-now” recollection of something previously known, but momentarily confused or forgotten. The analyses reveal that this practice typically occurs as part of a larger sequential pattern that the participants orient to and which serves as a procedure for dealing with, and generating an account for, one participant’s production of an inapposite action. As will be shown, the instantiation and progressive realization of this sequential procedure requires local inferential work from the participants. While some facets of this inferential work appear to be shaped by the particular context of the ongoing interaction, others are integral to the workings of the sequence as such. Moreover, the analyses suggest that participants’ understanding of oh that’s right as embodying an implicit memory claim rests on an inference which is based on a kind of semantic-pragmatic compositionality. The paper thus illustrates how inferences in conversational interaction can be systematically studied and points to the merits of combining an interactional and a linguistic perspective.