The rulebook states that a character can improve a special ability just like any other skill. But it also states that the character can become trained (or specialized) in any skill but attack or defense.
What rule do I apply if I want to improve attack abilities such as "Bash" or "Pierce"?
Abilities like Bash or Pierce may also be Trained or even Specialized on, as they are Special Abilities (Core Rulebook, pg.21).
SPECIAL ABILITIES
Character types and foci grant PCs special abilities at each new tier. Using these abilities usually costs points from your stat Pools; the cost is listed in parentheses after the ability name.
They work as normal, when using that ability, you reduce the difficulty by one step (or two if Specialized), as explained under Character Tiers and Benefits: Skills (Core Rulebook, pg.18):
The skill you choose for this benefit can be anything you wish, such as climbing, jumping, persuading, or sneaking. You can also choose to be knowledgeable in a certain area of lore, such as history or geology. You can even choose a skill based on your character’s special abilities. For example, if your character can make an Intellect roll to blast an enemy with mental force, you can become trained in using that ability, treating its difficulty as one step lower than normal.
So, if you decide to become Trained in Bash, all your attacks using Bash will have the difficulty reduced by one step, but your other attacks will not be affected.
But you cannot become Trained in "attacks" or "defenses", as that is too general for the system.
In RPG hermeneutics, it is a common principle (though rarely explicitly spelled out in the rulebooks themselves) that the specific overrides the general. Following that rule, this means that you can't easily buy training in general attack, but you can buy training in the specific sub-type of attack. If you do that, you will have improved rolls with that specific attack ability (only), subject to the usual limits on stacking roll bonuses.
Of course, given the way such special attacks usually require spending points from one of your pools (and even with Edge reduction that has downsides), and often provide rather modest benefits in exchange for their costs, it's an open question about whether you should spend your previous training slots on such specific attack types even though you can.
