Automated reasoning about the design of effective visual problem representations is possible when we adopt the view that visual problem representations, along with the pemeptual procedures that humans use to manipulate them, can be described using information-processing models of the sort introduced by Newell and Simon (1972). This approach provides us not only with a means of characterizing visual problem representations in a formal syntax but also with a means of automatically mapping between "logical" and "perceptual" problem representations and procedures. An automated system called BOZ is described that begins with a logical problem representation and solution procedure, and generates an informationally-equivalent visual problem representation and procedure that allows the human user to obtain the solution more efficiently. BOZ’s representation mapping technique proceeds by: (1) replacing demanding logical inferences in the solution procedure with efficient perceptual inferences; and (2) structuring information the visual representation such that search is minimized. The extent to which the visual representations and procedures produced by BOZ agree with what users actually see and do is discussed.