Tactics Lore - indirectly, it increases weapon damage and critical chance, thus making Callous Execution hit harder, also increases Life Leech damage from the Draw Life mod and allows modification points.
Any weapon lore (such as Sword Weapons when the Inquisitor is wielding a sword) - will indirectly increase this combat art's execution speed, damage and chance to hit, and will allow the equippng of higher level weapons used to execute this combat art.
Combat Discipline will increase its Damage and reduce its regeneration time if this Combat Art is placed within a combo. This increase in Damage is direct; it increases the +xx% that the CA adds to base damage.
Speed Lore - will increase its chance to hit indirectly by increasing a player's attack rating.
This will significantly weaken an opponent (especially if Mortifying Pillory is modified to reduce the armor value of the opponent), as well as cause other enemies nearby to start attacking the opponent.
Finally, the Inquisitor should use Callous Execution (or the previously mentioned combo that includes Ruthless Mutilation).
Pros and Cons
Very high damage attack.
Fast attack animation.
Low regeneration time.
Can be used from a distance with long ranged weapons.
An attractive look when using swords and Dual wield.
Can target only one opponent, regardless of modifications.
The only exception to this rule is if an Inquisitor is using Dual Wield.
The Inquisitor will hit a nearby second opponent if he kills his first opponent with the first weapon.
As a weapon-based combat art, it has the potential to miss.