UMLR — Even if Use Cases need not have an actor, there is some ambiguity when there is an «include»d or «extension» use case

Even if Use Cases need not have an actor, there is some ambiguity when there is an «include»d or «extension» use case. Much of the use case literature says, that the actors of the base use case are automatically actors of the extension or inclusion. They also say that duplicating the actors, that is, connecting the base’s actors to the extension or inclusion, implies that these actors may be needed twice for the extension/inclusion. This approach of assuming that the base’s actors are actors of the extension/inclusion is natural when the use cases are detailed out in sequence diagrams, and is almost a necessity when the extension/included use case can be used by many base use cases (where their actors could be different in each case). If an explicit actor is added to the extension/inclusion, is it added to the base’s actor or replace it?