On the correspondence between knowledge structures and attribution functions

Abstract

In this paper, the completeness (completion) of attribution functions is introduced and a general way is given to derive an attribution function from a knowledge structure on an arbitrary domain. With the help of these, this paper establishes a Galois connection (f,g) between the collection K of all knowledge structures and the collection F of all attribution functions, where knowledge spaces and complete attribution functions are closed elements of (f,g) in K and F, respectively. In addition, this paper introduces the reduct of attribution functions to give a direct characterization of granular attribution functions, which answers an open problem posed by Falmagne and Doignon (2011).