
## 3 A Definition Of Machine Intelligence

"Indeed the guiding inspiration of cognitive science is that at a suitable level of abstraction, a theory of natural intelligence should have the same basic form as the theories that explain sophisticated computer systems."
- J. Haugeland [Hau81]
Having presented a very general informal definition of intelligence in Subsection 2.6, we will now proceed to formalise this definition mathematically in a way that is appropriate for machines. We will then study some of the properties of this definition in the remainder of this section.

## 3.1 Basic Agent-Environment Framework Consider Again Our Informal Definition Of Intelligence:

Intelligence measures an agent's ability to achieve goals in a wide range of environments.

This definition contains three essential components: An agent, environments and goals.

Clearly, the agent and the environment must be able to interact with each other, specifically, the agent needs to be able to send signals to the environment and also receive signals being sent from the environment. Similarly, the environment must be able to receive and send signals to the agent. In our terminology we will adopt the agent's perspective on these communications and refer to the signals sent from the agent to the environment as actions, and the signals sent from the environment to the agent as perceptions.

Our definition of an agent's intelligence also requires there to be some kind of goal for the agent to try to achieve. Perhaps an agent could be intelligent, in an abstract sense, without having any objective to apply its intelligence to. Or perhaps the agent has no desire to exercise its intelligence in a way that effects its environment. In either case, the agent's intelligence would be unobservable and, more importantly, of no practical consequence. Intelligence then, at least the concrete kind that interests us, comes into effect when the agent has an objective that it actively pursues by interacting with its environment. Here we will refer to this objective as its goal.

The existence of a goal raises the problem of how the agent knows what the goal is.

One possibility would be for the goal to be known in advance and for this knowledge to be built into the agent. The problem with this however is that it limits each agent to just one goal. We need to allow agents that are more flexible, specifically, we need to be able to inform the agent of what the goal is. For humans this is easily done using language. In general however, the possession of a sufficiently high level of language is too strong an assumption to make about the agent. Indeed, even for something as intelligent as a dog or a cat, direct explanation is not very effective.

Fortunately there is another possibility which is, in some sense, a blend of the above two. We define an additional communication channel with the simplest possible semantics: A signal that indicates how good the agent's current situation is. We will call this signal the reward. The agent's goal is then simply to maximise the amount of reward it receives. So in a sense its goal is fixed. This is not particularly limiting however, as we have not said anything about what causes different levels of reward to occur. In a complex setting