Successful Visual Human-Computer Interaction is Undecidable

We propose a model of visual interactive computing and define a family of visual languages which abstract some of its features. We prove that the problem whether or not successful communications exist is not decidable. (A human-computer communication by means of a visual language is successful when all human commands, in the form of pictures composed of icons, are correctly interpreted and answered by the computer.) The proof makes use of a codification of the Post Correspondence Problem by means of icons and pictures. This result warns about possible limitations of a purely algorithmic treatment of interactive computing via visual languages