Knowledge Structures, Knowledge Spaces

In order to characterize a participants knowledge a knowledge state with respect to some problem set is defined as follows:

This definition states that any problem which is surmised by a mastered problem is also an element of the state , if is already in that state.

Definition:

Let be a set of problems ordered with a surmise relation . The set of all states which correspond to the surmise relation is called a knowledge structure.

The knowledge structure for this figure is

is closed under union and under intersection. Such a knowledge structure is called a quasi-ordinal knowledge space.

• closure under union is a plausible property of a set of states because it seems reasonable that, for example, in a group of participants knowledge can be accumulated by interaction.
• closure under intersection is too strict a property.
• for many applications knowledge structures resulting from surmise relations are completely sufficient in order to describe the behavior of participants.