A relation is often written as a table:

This can be represented using a relation $scheduled(Course,Section,Time,Room)$, with the knowledge base containing the facts

Suppose the relation $enrolled(StudentNum,Course,Section)$ is also defined by facts. The relation $busy(StudentNum,Time)$, which is the join of these relations, projected into student number and time, can be represented using the rule

A student is busy at a time if they are enrolled in a section of a course that is scheduled at that time.

Example 5.8 represented the electrical environment of Figure 5.2 using propositions. Using individuals and relations can make the representation more intuitive, because the general knowledge about how switches work can be clearly separated from the knowledge about a specific house.

To represent this domain, the first step is to decide what individuals exist in the domain. In what follows, assume that each switch, each light, and each power outlet is an individual. Each wire between two switches and between a switch and a light is also an individual. Someone may claim that, in fact, there are pairs of wires joined by connectors and that the electricity flow must obey Kirchhoff’s laws. Someone else may decide that even that level of abstraction is inappropriate because the flow of electrons should be modeled. However, an appropriate level of abstraction is one that is useful for the task at hand. A resident of the house may not know the whereabouts of the connections between the individual strands of wire or even the voltage. Therefore, let’s assume a flow model of electricity, where power flows from the outside of the house through wires to lights. This model is appropriate for the task of determining whether a light should be lit or not, but it may not be appropriate for other tasks.

Next, give names to each individual to which you want to refer. This is done in Figure 5.2 by writing the name next to the component. For example, the individual $w_0$ is the wire between light $l_1$ and switch $s_2$.

Next, choose which relationships to represent. Assume the following predicates with their associated intended interpretations:

• •

  $light(L)$ is true if the individual denoted by $L$ is a light.

• •

  $lit(L)$ is true if the light $L$ is lit and emitting light.

• •

  $live(W)$ is true if there is power coming into $W$; that is, $W$ is live.

• •

  $up(S)$ is true if switch $S$ is up.

• •

  $down(S)$ is true if switch $S$ is down.

• •

  $ok(E)$ is true if $E$ is not faulty; $E$ can be either a circuit breaker or a light.

• •

  $connected\mathrm{\_}to(X,Y)$ is true if component $X$ is connected to $Y$ such that current would flow from $Y$ to $X$.

At this stage, the computer has not been told anything. It does not know what the predicates are, let alone what they mean. It does not know which individuals exist or their names.

Before anything about the particular house is known, the system can be told general rules such as

This means that a light is lit if it has electricity coming in and is not broken.

Recursive rules let you state what is live from what is connected to what:

This specifies that there is electricity coming into the building, and if there is electricity coming into $Y$ and $X$ is connected to $Y$, then there will be electricity coming into $X$. Note that the order of clauses and the order of the elements of the body has no effect on the semantics.

For the particular house and configuration of components and their connections, the following facts about the world can be told to the computer:

These rules and atomic clauses are all that the computer is told. It does not know the meaning of these symbols. However, it can now answer queries about this particular house.