(21th-February-2020)
The representation scheme dimension concerns how the world is described.
The different ways the world could be to affect what an agent should do are called states. We can factor the state of the world into the agent's internal state (its belief state) and the environment state.
At the simplest level, an agent can reason explicitly in terms of individually identified states.
For example, A thermostat for a heater may have two belief states: off and heating. The environment may have three states: cold, comfortable, and hot. There are thus six states corresponding to the different combinations of belief and environment states. These states may not fully describe the world, but they are adequate to describe what a thermostat should do. The thermostat should move to, or stay in, heating if the environment is cold and move to, or stay in, off if the environment is hot. If the environment is comfortable, the thermostat should stay in its current state. The agent heats in the heating state and does not heat in the off state.
Instead of enumerating states, it is often easier to reason in terms of the state's features or propositions that are true or false of the state. A state may be described in terms of features, where a feature has a value in each state.
An agent that has to look after a house may have to reason about whether light bulbs are broken. It may have features for the position of each switch, the status of each switch (whether it is working okay, whether it is shorted, or whether it is broken), and whether each light works. The feature pos_s2 may be a feature that has value up when switch s2 is up and has value down when the switch is down. The state of the house's lighting may be described in terms of values for each of these features.
A proposition is a Boolean feature, which means that its value is either true or false. Thirty propositions can encode 230= 1,073,741,824 states. It may be easier to specify and reason with the thirty propositions than with more than a billion states. Moreover, having a compact representation of the states indicates understanding, because it means that an agent has captured some regularities in the domain.
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