Computer science has recently begun to formalize parallel processes so that it is sometimes possible to prove that a system of parallel processes will meet its specifications. However, the knowledge available to a robot of the other processes going on in the world will rarely take the form of a Petri net or any of the other formalisms used in engineering or computer science. In fact, anyone who wishes to prove correct an airline reservation system or an air traffic control system must use information about the behavior of the external world that is less specific than a program. Nevertheless, the formalisms for expressing facts about parallel and indeterminate programs provide a start for axiomatizing concurrent action. A robot must be able to express knowledge about space, and the locations, shapes and layouts of objects in space.
Present programs treat only very special cases.
A few are more sophisticated, but the objects must have simple geometric shapes. A formalism capable of representing the geometric information people get from seeing and handling objects has not, to my knowledge, been approached. The difficulty in expressing such facts is indicated by the limitations of English in expressing human visual knowledge. We can answer many more questions in the presence of a scene than we can from memory. The relation between three dimensional objects and their two dimensional retinal or camera images is mostly untreated.