The role mining problem is a wrong way to go when trying to solve the role definition problem. There is a need to distinguish between actual and potential/candidate roles.
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The actual roles are a complete and definite set that have semantics in the considered organizational context.
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The role mining problem will define a set of potential roles. We can only come with an incomplete solution to the role mining problem. By means of approximation and heuristic, we could find an almost optimal solution or one that works reasonably well, so a subset of the all the potential roles.
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Whereas all the actual roles set are assumed to exist and be useful in an enterprise context from the set of candidate roles a overwhelming majority will be eliminated.
So instead of trying to find all roles, why not just redefine the problem and take into consideration the correct premises to derive the set of correct roles. It all comes in the end to the old saying, why buy the cow (i.e. define the set of ALL candidate roles) when you can have the milk for free (i.e. the actual roles)?
