Ranked Interpretation

Heuristic information can be represented semantically, by taking the set of all valuations (which corresponds to states of the system) and ordering these from "most normal" to "least normal". Since the ordering indicates the states that are most normal, the agent can test sentences to see whether they are true in the most normal states.



A pre-order relation can be defined, which is both reflexive and transitive to describe the relative "normality" of each pair of states. If some pairs are defined for a particular set of sentences S, we can say we have a PREORDER on S.

If all pre-order relations are defined we can say we have a TOTAL PREORDER on S. Total preorders are important because they tell us how to arrange all the elements into levels. For small sets S, it is often convenient to depict a pre-order visually, and the standard means for doing so is called the Hasse Diagram (pictured above).

The lower the element, the more normal is the element.

In the example above: (0,0) is the most normal, (1,0) and (1,1) are next, and the most rare is (0,1).