Reasoning using negation is known to be difficult for transformer-based language models. While previous studies have used the tools of psycholinguistics to probe a transformer's ability to reason over negation, none have focused on the types of negation studied in developmental psychology. We explore how well transformers can process such categories of negation, by framing the problem as a natural language inference (NLI) task. We curate a set of diagnostic questions for our target categories from popular NLI datasets and evaluate how well a suite of models reason over them. We find that models perform consistently better only on certain categories, suggesting clear distinctions in how they are processed.