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An ILP system: CProgol
CProgol uses a covering approach: It selects an example to be generalised and finds a consistent clause covering the example
Basic algorithm for CProgol:
Select an example to be generalized.
Build most-specific-clause. Construct the most specific clause that entails the example selected, and is within language restrictions provided. This is usually a definite clause with many literals, and is called the "bottom clause."
Find a clause more general than the bottom clause. This is done by searching for some subset of the literals in the bottom clause that has the "best" score.
Remove redundant examples. The clause with the best score is added to the current theory, and all examples made redundant are removed. Return to Step 1 unless all examples are covered.