For questions about AI problem solving in terms of approaches, theory, logic, and other aspects where the problem is well defined and the objective is to find a solution to the problem.
Problem solving in artificial intelligence is the study of how an AI can solve a given problem.
The usual approach to problem solving is state search. The problem was described as an initial state, conditions for a final state, and a set of transition rules. A transition rule changes takes a state as input and outputs a new state.
The solution of the problem then consists of applying the right transitions, until a state is reached where that satisfies the condition for a final state.
As a concrete example, there is the problem of the Farmer, the Goat, the Cabbage and the Wolf. The farmer must row each of these to the other side of a river, but his boat is only big enough that he can transport only one of them at a time. If he leaves the goat with the cabbage, the goat will eat the cabbage; if he leaves the wolf with the goat, the wolf will eat the goat.
The initial state has the farmer, cabbage, goat and wolf on one side of the river. A final state has them all on the other side. The transition rules are all "row the cabbage OR the goat OR the wolf from the current side to the other".
There are several state search algorithms, where the purpose is to arrive at a final state in an efficient manner.