Surmise relations and quasiordinal knowledge spaces
- Thus, from the mastery of one problem the mastery of other problems
is assumed or `surmised'.
- Fundamental idea:
Dependency relations exist between problems of a set
`If a participant is capable of mastering a problemthen he or she will also be capable of mastering some problems
and
.'
Definition:
-
Let
be a set of problems. A reflexive and transitive binary relation 
on
is said to be a surmise relation. A set
ordered by such a relation is called a surmise ordered problem
set.
Binary Relations:
- A binary relation among a set of objects such as the surmise relation can be formalized as follows.
Definition:
Let P be a set. A binary relation on this set is a subset of the Cartesian product P x P.
- The relation is a set of ordered pairs.
- If
and 
are elements of P which are in the relation R then the
following notation applies: 
- A relation with special properties is the surmise relation.
- Some other types of relations are also possible.
Example:
Consider a set
with four problems, and a surmise relation
Figure 1: Upward drawing (Hasse diagram) for the example problem set
