Whenever the present theory of YAILS (which can be empty) doesn't fulfill the completeness criterion YAILS needs to invent new rules inorder to raise the coverage of the theory. This invention process is again a search through the search space but this time there is a preference criterion on raising coverage. Of course this doesn't mean that the invented rules don't have those "nice" properties referred above.
The process of invention of new rules is iterative. It stops whenever the completeness criterion is fulfilled. Each iteration has three major steps :- finding an example to cover; obtaining a starting point for the search; start the search procedure. The first step is done by just picking the head of the list of uncovered examples. The second involves choosing one of the selectors of the previously choosed example. For that purpose it is chose the one with highest consistency (see appendix A for a definition of consistency). The justification for that is the tentative of shorten up the following search procedure. Finally the search procedure is basically the same as the one referred before but with the specialization process being different. In effect during invention of rules the main goal is to cover the example chosen on the first step, so the specialization is restricted to new complexes that still cover the example.