Perception and Experience in Problem Solving

Abstract

Whilst much emphasis in AI has been placed on the use of goals in problem solving, less emphasis has been placed on the role of perception and experience. In this paper we show that in the domain that may be considered the most abstract, namely mathematics, that perception and experience play an important role. The mathematician has a vast amount of mathematical knowledge, and yet is able to utilise the appropriate knowledge without difficulty. We argue that it is essential to model how well the knowledge is grasped, so that mathematical knowledge can grow from partial knowledge to important results that are easily accessed. Not all knowledge is equal in its importance, and we argue that perception and experience play a key role in ordering our knowledge. Features play a role in both representing the information from the environment, and indexing the knowledge of our memories, but a key requirement is that the features should be dynamic and not be built in. This research is implemented in the program MU, the Mathematics Understander, which utilises the CMS, Contextual Memory System. MU has sucessfully "read" university level texts in pure mathematics, checking the proofs and solving the simple problems.