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 (Thomas 2012; Altshuler & Schwarzschild 2013; Musan 1995; Magri 2009; 2011; Sudo & Romoli 2017). In the literature, there are two main proposals for capturing this asymmetry: one assumes a difference in informativity between the past and present counterparts mentioned above (Altshuler & Schwarzschild 2013), while the other proposes a structural difference between the two (Thomas 2012). The two approaches are similar in terms of their empirical coverage, but they differ in the predictions they make for language acquisition. We used a novel animated picture selection paradigm (building on Katsos & Bishop 2011) to investigate the predictions of the two approaches to temporal inferences. Specifically, we compared the performance of a group of 4–6-year-old children and a group of adults on temporal inferences, the "not all" scalar implicature of the quantifier "some", and inferences of adverbial modifiers under negation. The results of our experiment revealed that overall, children computed all three inference types at a lower rate than the adult controls, however they were more adult-like on temporal inferences and on the inferences of adverbial modifiers than on the scalar implicature of “some”. We discuss the implications of the findings, both for a developmental alternatives-based hypothesis, which posits that children’s difficulties with certain implicatures arise from a difficulty in accessing the required lexical alternatives (e.g., Barner et al. 2011; Tieu et al. 2016; 2017; Singh et al. 2016), 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).