“Which picture is worth which 1000 words?” The best known theories approach this question through explanations in terms of human computational architecture. So, for Larkin & Simon , diagrams are efficacious because they allow the parallel computational power of human vision to be brought to bear on diagrammatic representations (at least in some cases).
A more fundamental approach separates the problem into two parts—issues about computational complexity arising from the nature of the semantic interpretation (issues which are abstract with regard to architecture); and issues about how human computational architecture in particular can be brought to bear on different representations. On this view, diagrams are often logically inexpressive and this is why they lead to efficient inference. Indeed, this is part of the reason why parallel computational mechanisms may be applicable to them.
This paper reviews experiences of applying this semantic approach to the empirical study of modality assignment in disparate domains (logic teaching, safety critical software engineering and the teaching of formality) and draws together some conclusions concerning the multifarious implications of formality for HCI.