General 'combat damage' applies to and affects all Attributes Scores. More specific penalties are usually handled through Demon Abilities like Daze. [1]

Penalties resulting from such rolls are focused on specific types of conflicts, not on scores. If you wanted to create a Demon Ability that applied a penalty to the target's social interaction (for instance), it would be appropriate to create a variant of Daze that would inflict penalties in any socially manipulative situation regardless of what score the victim is using (in the same way that Daze applies penalties to all Perception rolls, regardless of the base Score being used).

For instance:

__Pariah__

The user hits the target with a combat roll to subtract Power from all the target's social interaction rolls; the effect lasts for a few minutes (Demon's Power?), but that 'timer' does not generally go into play until the target enters a social situation.

A better way to put it may be to simply open up Daze to affect any single class of actions, not a specific Score -- actually, altering Daze to a rules-set like Travel, with a list of available categories that it may affect, would be a good idea. [2]