| A key step in the application of Knowledge Spaces theory is the construction of an accurate knowledge structure. A number of algorithms, such as QUERY (Koppen, 1993; Koppen and Doignon, 1990; see also Dowling, 1993; Müller 1989), have been designed to build a knowledge structure by interviewing experts. Though efficient at making logical inferences, these algorithms have no provision for careless or judgment errors by the expert and tend to amplify the effect of such errors through numerous derivations. In the light of these shortcomings, several authors (Kambouri et aL, 1994; Schrepp and Held, 1995; Cosyn and Thiéry, 2000) pointed to the need for empirical validation of a knowledge structure. In this dissertation, we address the issue of gradually improving the accuracy of a knowledge structure, a process that we call ‘adaptation’ of knowledge structures. The focus of our approach is to set in place mechanisms capable of constantly adjusting a knowledge structure while it is used and empirical data is collected. A main source of data is the results obtained from assessing individuals. By introducing some redundancy in the questioning of these individuals, we can design algorithms that gradually improve a knowledge structure. Three classes of procedures are presented: ‘refinement’ of a knowledge structure, multiple stage improvement using the concept of ‘rim’ of a knowledge structure, and gradual ‘adaptation’ by evolving within the ‘fringes’ of a ‘well-graded’ knowledge space. Much of our efforts have been centered on the mathematical (in particular, combinatoric) foundation of these procedures. A key result, is that the set of all ‘well-graded’ ‘discriminative’ families which are closed under union is ‘path-connected’. This result is important because it proves that ‘well-graded’ ‘discriminative’ knowledge spaces have non-empty ‘fringes’, and that any ‘well-graded’ ‘discriminative’ knowledge space can be transformed gradually (by adding only one knowledge state at a time) into any other ‘well-graded’ ‘discriminative’ knowledge space which includes it. A link can be made between these approaches and the objective of improving the functioning of a system through empirical data, or Machine Learning, as it is called in Artificial Intelligence. |
