Let Q be a finite set of problems. A knowledge state is the set of pro
blems a person is capable of solving. A family K of knowledge states i
s called a knowledge structure if the empty set and Q are elements of
K. When it is closed under union, the structure is called a knowledge
space. There exist effective algorithms to generate a knowledge space
by querying an expert using an entail relation. In this paper we show
that more general knowledge structures can be generated using modified
query procedures. The general theory of the Galois connections betwee
n entail relations and knowledge structures is explored. Finally, we p
resent query procedures which can be applied to generate any knowledge
structure. (C) 1996 Academic Press, Inc.