The automatic synthesis of biomedical publications catalyzes a profound research interest elicited by literature congestion. Current sequence-to-sequence models mainly rely on the lexical surface and seldom consider the deep semantic interconnections between the entities mentioned in the source document. Such superficiality translates into fabricated, poorly informative, redundant, and near-extractive summaries that severely restrict their real-world application in biomedicine, where the specialized jargon and the convoluted facts further emphasize task complexity. To fill this gap, we argue that the summarizer should acquire semantic interpretation over input, exploiting structured and unambiguous representations to capture and conserve the most relevant parts of the text content. This paper presents CogitoErgoSumm, the first framework for biomedical abstractive summarization equipping large pre-trained language models with rich semantic graphs. Precisely, we infuse graphs from two complementary semantic parsing techniques with different goals and granularities—Event Extraction and Abstract Meaning Representation, also designing a reward signal to maximize information content preservation through reinforcement learning. Extensive quantitative and qualitative evaluations on the CDSR dataset show that our solution achieves competitive performance according to multiple metrics, despite using 2.5x fewer parameters. Results and ablation studies indicate that our joint text-graph model generates more enlightening, readable, and consistent summaries. Code available at: https://github.com/disi-unibo-nlp/cogito-ergo-summ.