Third edition of Artificial Intelligence: foundations of computational agents, Cambridge University Press, 2023 is now available (including the full text).

1.4.2 Representations

Once you have some requirements on the nature of a solution, you must represent the problem so a computer can solve it.

Computers and human minds are examples of physical symbol systems. A symbol is a meaningful pattern that can be manipulated. Examples of symbols are written words, sentences, gestures, marks on paper, or sequences of bits. A symbol system creates, copies, modifies, and destroys symbols. Essentially, a symbol is one of the patterns manipulated as a unit by a symbol system. The term physical is used, because symbols in a physical symbol system are physical objects that are part of the real world, even though they may be internal to computers and brains. They may also need to physically affect action or motor control.

Much of AI rests on the physical symbol system hypothesis of Newell and Simon (1976):

A physical symbol system has the necessary and sufficient means for general intelligent action.

This is a strong hypothesis. It means that any intelligent agent is necessarily a physical symbol system. It also means that a physical symbol system is all that is needed for intelligent action; there is no magic or an as-yet-to-be-discovered quantum phenomenon required. It does not imply that a physical symbol system does not need a body to sense and act in the world. The physical symbol system hypothesis is an empirical hypothesis that, like other scientific hypotheses, is to be judged by how well it fits the evidence, and what alternative hypotheses exist. Indeed, it could be false.

An intelligent agent can be seen as manipulating symbols to produce action. Many of these symbols are used to refer to things in the world. Other symbols may be useful concepts that may or may not have external meaning. Yet other symbols may refer to internal states of the agent.

An agent can use physical symbol systems to model the world. A model of a world is a representation of the specifics of what is true in the world or of the dynamic of the world. The world does not have to be modeled at the most detailed level to be useful. All models are abstractions; they represent only part of the world and leave out many of the details. An agent can have a very simplistic model of the world, or it can have a very detailed model of the world. The level of abstraction provides a partial ordering of abstraction. A lower-level abstraction includes more details than a higher-level abstraction. An agent can have multiple, even contradictory, models of the world. The models are judged not by whether they are correct, but by whether they are useful.

Example 1.2: A delivery robot can model the environment at a high level of abstraction in terms of rooms, corridors, doors, and obstacles, ignoring distances, its size, the steering angles needed, the slippage of the wheels, the weight of parcels, the details of obstacles, the political situation in Canada, and virtually everything else. The robot could model the environment at lower levels of abstraction by taking some of these details into account. Some of these details may be irrelevant for the successful implementation of the robot, but some may be crucial for the robot to succeed. For example, in some situations the size of the robot and the steering angles may be crucial for not getting stuck around a particular corner. In other situations, if the robot stays close to the center of the corridor, it may not need to model its width or the steering angles.

Choosing an appropriate level of abstraction is difficult because

  • a high-level description is easier for a human to specify and understand.
  • a low-level description can be more accurate and more predictive. Often high-level descriptions abstract away details that may be important for actually solving the problem.
  • the lower the level, the more difficult it is to reason with. This is because a solution at a lower level of detail involves more steps and many more possible courses of action exist from which to choose.
  • you may not know the information needed for a low-level description. For example, the delivery robot may not know what obstacles it will encounter or how slippery the floor will be at the time that it must decide what to do.

It is often a good idea to model an environment at multiple levels of abstraction. This issue is further discussed in Section 2.3.

Biological systems, and computers, can be described at multiple levels of abstraction. At successively lower levels are the neural level, the biochemical level (what chemicals and what electrical potentials are being transmitted), the chemical level (what chemical reactions are being carried out), and the level of physics (in terms of forces on atoms and quantum phenomena). What levels above the neuron level are needed to account for intelligence is still an open question. Note that these levels of description are echoed in the hierarchical structure of science itself, where scientists are divided into physicists, chemists, biologists, psychologists, anthropologists, and so on. Although no level of description is more important than any other, we conjecture that you do not have to emulate every level of a human to build an AI agent but rather you can emulate the higher levels and build them on the foundation of modern computers. This conjecture is part of what AI studies.

The following are two levels that seem to be common to both biological and computational entities:

  • The knowledge level is a level of abstraction that considers what an agent knows and believes and what its goals are. The knowledge level considers what an agent knows, but not how it reasons. For example, the delivery agent's behavior can be described in terms of whether it knows that a parcel has arrived or not and whether it knows where a particular person is or not. Both human and robotic agents can be described at the knowledge level. At this level, you do not specify how the solution will be computed or even which of the many possible strategies available to the agent will be used.
  • The symbol level is a level of description of an agent in terms of the reasoning it does. To implement the knowledge level, an agent manipulates symbols to produce answers. Many cognitive science experiments are designed to determine what symbol manipulation occurs during reasoning. Note that whereas the knowledge level is about what the agent believes about the external world and what its goals are in terms of the outside world, the symbol level is about what goes on inside an agent to reason about the external world.