There is substantial support for the general idea that a formalization of comprehenders' expectations about the likely next word in a sentence helps explaining data related to online sentence processing. While much research has focused on syntactic, semantic, and discourse expectations, the present event‐related potentials (ERPs) study investigates neurolinguistic correlates of pragmatic expectations, which arise when comprehenders expect a sentence to conform to Gricean Maxims of Conversation. For predicting brain responses associated with pragmatic processing, we introduce a formal model of such Gricean pragmatic expectations, using an idealized incremental interpreter. We examine whether pragmatic expectancies derived from this model modulate the amplitude of the N400, a component that has been associated with predictive processing. As part of its parameterization, the model distinguishes genuine pragmatic interpreters, who expect maximally informative true utterances, from literal interpreters, who only expect truthfulness. We explore the model's non‐trivial predictions for an experimental setup which uses picture‐sentence verification with ERPs recorded at several critical positions in sentences containing the scalar implicature trigger some. We find that Gricean expectations indeed affect the N400, largely in line with the predictions of our model, but also discuss discrepancies between model predictions and observations critically.