A Computational Framework for Granularity and Its Application to Educational Diagnosis

Abstract

Many artificial intelligence systems implicitly use notions of granularity in reasoning, but there is very little research into granularity itself. An exception is the work of Hobbs [1985], which outlines several characteristics of granularity. In this paper we describe an approach to representing granularity which formalizes in computational terms most of Hobbs' notions, often refining and extending them. In particular two types of granularity have been delineated: aggregation and abstraction. Objects can be described at various grain sizes and connected together into a granularity hierarchy which allows focus shifts along either aggregation or abstraction dimensions. We briefly discuss how we have used granularity hierarchies in the recognition of novice LISP programming strategies and show how this enhances the recognition process and can lead toward planning appropriate feedback for the student.