The first step in the design of RP or MP is to decide what structure the world is to be regarded as having, and how information about the world and its laws of change are to be represented in the machine. This decision turns out to depend on whether one is talking about the expression of general laws or specific facts. Thus, our understanding of gas dynamics depends on the representation of a gas as a very large number of particles moving in space; this representation plays an essential role in deriving the mechanical, thermal electrical and optical properties of gases. The state of the gas at a given instant is regarded as determined by the position, velocity and excitation states of each particle. However, we never actually determine the position, velocity or excitation of even a single molecule. Our practical knowledge of a particular sample of gas is expressed by parameters like the pressure, temperature and velocity fields or even more grossly by average pressures and temperatures. From our philosophical point of view this is entirely normal, and we are not inclined to deny existence to entities we cannot see, or to be so anthropocentric as to imagine that the world must be so constructed that we have direct or even indirect access to all of it.
From the artificial intelligence point of view we can then define three kinds of adequacy for representations of the world.
A representation is called metaphysically adequate if the world could have that form without contradicting the facts of the aspect of reality that interests us. Examples of metaphysically adequate representations for different aspects of reality are:
1. The representation of the world as a collection of particles interacting through forces between each pair of particles.
2. Representation of the world as a giant quantum-mechanical wave function.
3. Representation as a system of interacting discrete automata. We shall make use of this representation.
Metaphysically adequate representations are mainly useful for constructing general theories. Deriving observable consequences from the theory is a further step.
A representation is called epistemologically adequate for a person or machine if it can be used practically to express the facts that one actually has about the aspect of the world. Thus none of the above-mentioned representations are adequate to express facts like `John is at home' or `dogs chase cats' or `John's telephone number is 321-7580'. Ordinary language is obviously adequate to express the facts that people communicate to each other in ordinary language. It is not, for instance, adequate to express what people know about how to recognize a particular face. The second part of this paper is concerned with an epistemologically adequate formal representation of common-sense facts of causality, ability and knowledge.
A representation is called heuristically adequate if the reasoning processes actually gone through in solving a problem are expressible in the language. We shall not treat this somewhat tentatively proposed concept further in this paper except to point out later that one particular representation seems epistemologically but not heuristically adequate.
In the remaining sections of the first part of the paper we shall use the representations of the world as a system of interacting automata to explicate notions of causality, ability and knowledge (including self-knowledge).