Knowledge compilation studies representations of Boolean formulas. An important task is to map out the pros and cons of various representations. In particular, we study the trade-off between the size of representations and the supported queries and transformations. In this talk, we focus on one method for proving lower bounds on representation size. This involves studying so-called combinatorial rectangles: an important concept from communication complexity. The talk will build up to discussing a recent result showing that structured d-DNNF does not support polynomial time negation. As such the content is loosely based on the forthcoming paper "Structured d-DNNF is Not Closed Under Negation" [IJCAI, 2024]. A preprint is available at: