Sentences involving past tense verbs, such as “My dogs were on the carpet”, tend to give rise to the inference that the corresponding present tense version, “My dogs are on the carpet”, is false. This inference is often referred to as a cessation or temporal inference, and is generally analyzed as a type of implicature. There are two main proposals for capturing this asymmetry: one assumes a difference in informativity between the past and present counterparts (Altshuler & Schwarzschild 2013), while the other proposes a structural difference between the two (Thomas 2012). The two approaches are similar in terms of empirical coverage, but differ in their predictions for language acquisition. Using a novel animated picture selection paradigm, we investigated these predictions. Specifically, we compared the performance of a group of 4–6-year-old children and a group of adults on temporal inferences, scalar implicatures arising from “some”, and inferences of adverbial modifiers under negation. The results revealed that overall, children computed all three inferences at a lower rate than adult controls; however they were more adult-like on temporal inferences and inferences of adverbial modifiers than on scalar implicatures. We discuss the implications of the findings, both for a developmental alternatives-based hypothesis (e.g., Barner et al. 2011; Singh et al. 2016; Tieu et al. 2016; 2018), as well as theories of temporal inferences, arguing that the finding that children were more (and equally) adult-like on temporal inferences and adverbial modifiers supports a structural theory of temporal inferences along the lines of Thomas (2012).