All 6 Uses of

resolve
in
The Adventures of Tom Sawyer

They inwardly resolved to watch him nights, when opportunity should offer, in the hope of getting a glimpse of his dread master.
Chpt 11

resolved = decided

The other pirates envied him this majestic vice, and secretly resolved to acquire it shortly.
Chpt 13

So they inwardly resolved that so long as they remained in the business, their piracies should not again be sullied with the crime of stealing.
Chpt 13

She resolved to let him get whipped on the damaged spelling-book's account, and to hate him forever, into the bargain.
Chpt 18

They resolved to keep a lookout for that Spaniard when he should come to town spying out for chances to do his revengeful job, and follow him to "Number Two," wherever that might be.
Chpt 26

Definitions:

(1) (resolve as in: I resolved to stop drinking.)
to decide -- typically a firm or formal decision

In modern writing resolve is typically used to emphasize a firm or formal decision. In classic literature, it is used more frequently and often simply replaces decide or determine.
(2) (resolve as in: This committee hereby resolves...)
make a decision or voice an opinion by formal group vote
(3) (resolve as in: Her resolve weakened.)
firmness of purpose (strong determination to do something)
(4) (resolve as in: How was the problem resolved?)
to solve a problem, settle a disagreement, or for a situation to change
(5) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Less commonly, resolve can mean:
- to make clearly visible -- as in "The microscope cannot resolve that level of detail."
- to divide into parts -- as in "The problem resolves into three parts,"or (math) "Resolve the polynomial into factors," or (chemistry) "As the temperature changes, the compound resolves into its component parts," or (physics) "The force on the inclined plane resolves into horizontal and vertical components."
- reduce or convert into something else -- as in "The URL is resolved to an IP address," or (music) "The progression is resolved as the dissonance is replaced by consonance."