Goal State
A goal state is a state of the world in which the problem solver's objective is satisfied, and the goal of a search problem is the set of all such states. It is one of the five components of a formal search problem, alongside the initial state, the actions, the transition model and the path cost, and it answers the question of when to stop. Without a precise statement of what counts as success, a search procedure has nothing to aim for, no way to recognize arrival, and no way to compare one solution with another. The notion looks trivial in a puzzle and turns out to be one of the more delicate ideas as soon as goals are vague, plural or open to interpretation.
A goal can be given as an explicit description or as a test, and the difference is one of how much the designer knows in advance. In the 8-puzzle the goal is a single named arrangement of tiles, so the check is simple equality. In chess there is no list of winning positions; instead a test (is the opponent's king in check with no legal escape?) classifies any position as won or not. In route planning a goal is a destination, but the same problem can be framed with a set of acceptable destinations, any airport in a region, say. The test form is more general and usually more compact, since it can describe a huge or infinite set of states without listing them, and it is what search algorithms actually call at each expansion. In STRIPS, introduced by Richard Fikes and Nils Nilsson in 1971, a goal is a logical condition that a state must satisfy, which again describes a set of states rather than one.
Goal formulation is a step distinct from solving, and it is often the real act of intelligence. In the standard account in artificial intelligence textbooks, the agent first decides which goal to adopt, using its current situation and what its performance measure rewards, because adopting a goal narrows the options it must consider. Goals are also not guaranteed to be single or consistent. An agent may hold several at once, such as reaching a meeting on time, spending little and avoiding tolls, and these may conflict, so they must be combined into a cost function, ranked, or handled by satisfying some and trading off others. Multiple goal states are a different matter: when many states satisfy one objective, the search simply stops at the first or cheapest of them.
Goal states link to the broader idea of a goal-based agent, but the two should be kept apart. A goal state is a technical object inside a model: a point or region in a state space that a search algorithm can detect. A goal-based agent is a design: it selects actions by considering their consequences relative to goals, in contrast to a simple reflex agent that only reacts. Philosophers and agent designers have added more structure. Michael Bratman's 1987 book Intention, Plans, and Practical Reason argued that intentions are commitments that persist and constrain further reasoning, and this fed the belief-desire-intention architecture for software agents of the 1990s, in which goals are things the agent has adopted and may drop, not merely conditions to test.
The most common error is to treat the goal state as the answer. Often the goal state is already known and the answer is the path: in a puzzle the final arrangement is given, and the value lies in the sequence of moves. In other problems, such as constraint satisfaction, the goal state is itself the solution, and the path is irrelevant. A second pitfall is specification: a goal that is stated precisely but does not capture what the designer wanted will be achieved in unwanted ways. A cleaning robot told to have no visible mess can satisfy that test by hiding the mess. This difficulty, which grows with agent capability, is why reward and objective misspecification is a central concern of AI safety research.
Modern agents make the issue concrete. Language-model agents are given goals in natural language, which they must interpret, decompose into subgoals, and check against the outcomes of their own actions, so goal formulation, goal testing and the question of when a goal is genuinely met have all come back as practical engineering questions. In reinforcement learning the goal is carried by a reward signal and not an explicit test, and in robotics a goal may be a region of continuous space, not a discrete state. The classical definition remains the clearest way to see what is being asked of a system.
Read goal state as the formal statement of what success means: whether given as one state, a test or a condition, it is what search can recognize, and the quality of every plan depends on how faithfully it captures what was actually wanted.