While many formal frameworks distinguish between desires and intentions, and considerable empirical work shows that people interpret them differently, no studies examine how people reason about them. We extend Harner and Khemlani’s (2020) model-based theory of relations describing desire. The theory holds that people represent desires, as in, e.g., Pav wants to visit Angkor Wat, by pairing a factual representation of the negation of the desire (e.g., that Pav is not currently visiting Angkor Wat) with a future possibility where the desire is realized. We propose that intentions, which people express using verbs like plan, are represented as future actions that agents seek to perform. A particular individual’s plans must be consistent with one another, whereas desires can conflict with these plans. We show how the model theory distinguishes desires and intentions, namely that models can be coherent even when a desire and a plan are inconsistent with each other. The distinctions make predictions about how reasoners should assess the consistency of statements concerning desires and intentions, and we report on two experiments that validate them.