Machine Learning - DISCo

CHAPTER 12 COMBINING INDUCTIVE AND ANALYTICAL LEARNING 359
2. Create an operational, logically sufficient condition for the target concept
according to the domain theory. Add this set of literals to the current preconditions
of h. Finally, prune the preconditions of h by removing any literals
that are unnecessary according to the training data. The dashed arrow in
Figure 12.8 denotes this type of specialization.
The detailed procedure for the second operator above is as follows. FOCL
first selects one of the domain theory clauses whose head (postcondition) matches
the target concept. If there are several such clauses, it selects the clause whose
body (preconditions) have the highest information gain relative to the training
examples of the target concept. For example, in the domain theory and training
data of Figure 12.3, there is only one such clause:
Cup t Stable, Lifable, Openvessel
The preconditions of the selected clause form a logically sufficient condition for
the target concept. Each nonoperational literal in these sufficient conditions is
now replaced, again using the domain theory and substituting clause preconditions
for clause postconditions. For example, the domain theory clause Stable t
BottomIsFlat is used to substitute the operational BottomIsFlat for the unoperational
Stable. This process of "unfolding" the domain theory continues until the
sufficient conditions have been restated in terms of operational literals. If there
are several alternative domain theory clauses that produce different results, then
the one with the greatest information gain is greedily selected at each step of
the unfolding process. The reader can verify that the final operational sufficient
condition given the data and domain theory in the current example is
BottomIsFlat , HasHandle, Light, HasConcavity , ConcavityPointsUp
As a final step in generating the candidate specialization, this sufficient condition is
pruned. For each literal in the expression, the literal is removed unless its removal
reduces classification accuracy over the training examples. This step is included
to recover from overspecialization in case the imperfect domain theory includes
irrelevant literals. In our current example, the above set of literals matches two
positive and two negative examples. Pruning (removing) the literal HasHandle results
in improved performance. The final pruned, operational, sufficient conditions
are, therefore,
BottomZsFlat , Light, HasConcavity , ConcavityPointsUp
This set of literals is now added to the preconditions of the current hypothesis.
Note this hypothesis is the result of the search step shown by the dashed arrow
in Figure 12.8.
Once candidate specializations of the current hypothesis have been generated,
using both of the two operations above, the candidate with highest information
gain is selected. In the example shown in Figure 12.8 the candidate chosen
at the first level in the search tree is the one generated by the domain theory. The
search then proceeds by considering further specializations of the theory-suggested