Descriptive and Assessment Languages*

Abstract

How can we economically describe a state in a knowledge structure? The question is inescapable because, as pointed out earlier, realistic states will typically be quite large. In such cases, it is impractical to describe a state by giving the full list of items that it contains. It is also unnecessary: because of the redundancy in many real-life knowledge structures¹, a state will often be characterizable by a relatively small set of features. This idea is not new.In Chapter 4, we proved that any state in a well-graded knowledge structure could be fully described by simply listing its inner and outer fringes (cf. Theorem 4.1.7 and Remark 4.1.8(a)). Here, we consider this issue more systematically. This chapter is somewhat eccentric to the rest of this book and can be skipped without harm at first reading. We begin by illustrating the main ideas in the context of a simple example encountered earlier.