When an archer wielding an Adaptive composite longbow's strength is reduced below 10, should the archer suffer a -2 penalty to attacks for using a composite bow with a strength rating that is too high for the character to use effectively?
Here is the description of the Adaptive special quality:
An adaptive bow responds to the strength of its wielder, acting as a bow with a strength rating equal to its wielder’s Strength bonus. The wielder can fire it with a lesser Strength bonus (and cause less damage) if desired.
Here is the description for a composite bow when using a strength below the strength rating for the bow:
If your Strength bonus is less than the strength rating of the composite bow, you can’t effectively use it, so you take a –2 penalty on attacks with it.
The following was the closest I could find in the PFSRD for formal definitions for the following terms which I think are germane to the question (Italics were added by me):
The modifier is the number you apply to the die roll when your character tries to do something related to that ability.
A positive modifier is called a bonus
[A] negative modifier is called a penalty.
The situation that gave rise to this question
I am the DM for a group with an archer character. The character has a 14 Strength (+2 strength bonus). He purchased a +1 Composite Longbow with a +2 base Strength rating and the Adaptive property. Ordinarily, the archer applies +2 to damage from his strength bonus.
In a recent combat, the party wizard cast Reduce Person on the archer. While reduced, his Strength was only 12, reducing his bonus to damage to only +1. Because the bow is Adaptive, I assigned no penalty to the attack rolls. Then, the Skald inspired rage, increasing the archer's strength to 16. The bonus to damage likewise increased to +3, again because of the adaptive property. Then, the archer was the target of a nasty poison that caused 10 strength drain. This brought the archer's strength down to 6 with a modifier of -2. I made a ruling in the moment that the -2 penalty did apply. After the game, the player asked me to reconsider for the future.