We investigate reaction times for classification of visual stimuli composed of combinations of shapes, to distinguish between parallel and serial processing of stimuli. Reaction times in a visual XOR task are slower than in AND/OR tasks in which pairs of shapes are categorised. This behaviour is explained by the time needed to perceive shapes in the various tasks, using a parallel drift diffusion model. The parallel model explains reaction times in an extension of the XOR task, up to 7 shapes. Subsequently, the behaviour is explained by a combined model that assumes perceptual chunking, processing shapes within chunks in parallel, and chunks themselves in serial. The pure parallel model also explains reaction times for ALL and EXISTS tasks. An extension to the perceptual chunking model adds time taken to apply a logical rule. We are able to improve the fit to the data by including this extra parameter, but using model selection the extra parameter is not supported. We further simulate the behaviour exhibited using an echo state network, successfully recreating the behaviour seen in humans.