In chess, on the other hand, the goal is to reach a checkmate.
Another form of abstraction is to generalise a particular problem solving technique.
Often AI research progresses through a series of abstractions of this kind.
One form of abstraction that is very useful is to disregard particulars of a problem.
For instance, when designing an agent to find a route from one town to another, you ignore most of the details you may know about each town (population, weather, food, etc).
Suppose the problem we had set our agent was to find a name for a newborn baby, with some properties.
In this case, there are lists of "accepted" names for babies, and any solution must appear in that list, so goal-checking amounts to simply testing whether the name appears in the list.
Instead, a more abstract notion of checkmate is used, whereby our agent checks that the opponent's king cannot move without being captured.
Abstraction is an important tool for scientists in general, and AI practitioners in particular.
Rather, the point of the search is to find a path, so the agent must remember where it has been.
The answer is, of course: (FILL IN THIS GAP AS AN EXERCISE).