Reading Decision Trees

There is a link between decision tree representation and logical representations, which may be exploited to form it more easy  to understand and learned decision trees. If we assume about it, each decision tree is actually a disjunction of implications (if ... then statements), and the implications are Horn clauses: a conjunction of literals implying a single literal. In the above tree, we may notice this by reading from the root node to each leaf node:

If the parents are tripping, then go to the cinema

or

If the parents are not tripping and it is sunny, then go fortennis

or

If the parents are not tripping and it is windy and you're wealthy, then go for shopping

or

If the parents are not tripping and it is windy and you're poor, then go to cinema

or

If the parents are not tripping and it is rainy, then stay inside.

Of course, this is only a re-statement of the actual mental decision making method we defined. Remember, however, that we will be programming an agent to learn decision trees from example, so this sort of conditions will not happen as we will start with just example conditions. It will therefore be important for us to be able to read the decision tree the agent advises.

Decision trees don't have to be representations of decision forming methods, and they can equally use to categorization problems. If we phrase the above question slightly in different way, we may see this: instead of saying that we need to represent a decision method for what to do on a weekend, we might ask what sort of weekend this is: is it a weekend where we play tennis, or one where we go for shopping, or one where we watch a film, or one where we stay inside? For other example, we can refer back to the animals example from the previous lecture:  in that  case, we wished to categories what group an animal was (mammal, fish, reptile, bird) using physical features (whether it lays eggs, number of legs, etc.). This could simply be phrased as a question of learning a decision tree to choose which category a given animal is in, e.g., if it lays eggs and is homoeothermic, then it's a bird, and so on...