We aim to model the semantics of “but” in dialogue, focusing on cases in which it signals denial of expectation (DofE) across speakers. We present an algorithm that predicts the defeated expectation from the perspective of the hearer of the DofE, and we consider differences between task-oriented dialogue (TOD) and non-task-oriented dialogue (NTOD). We motivate this work by showing how it updates beliefs in an Information State (IS) model of dialogue and can be used to facilitate discourse understanding and natural language generation (NLG).