Typically, you know more about a domain than a database of facts; you know general rules from which other facts can be derived. Which facts are explicitly given and which are derived is a choice to be made when designing and building a knowledge base.

Primitive knowledge is knowledge that is specifies explicitly in terms of facts. Derived knowledge is knowledge that can be inferred from other knowledge. Derived knowledge is typically specified using rules.

The use of rules allows for a more compact representation of knowledge. Derived relations allow for conclusions to be drawn from observations of the domain. This is important because you do not directly observe everything about a domain. Much of what is known about a domain is inferred from the observations and more general knowledge.

A standard way to use derived knowledge is to put individuals into classes, and then give general properties to classes so that individuals inherit the properties of classes. Grouping individuals into classes enables a more concise representation because the members of a class can share the attributes they have in common (see the box). This is the same issue that was discussed in the context of probabilistic classifiers.

A class is the set of those actual and potential individuals that would be members of the class. This is typically an intensional set, defined by a characteristic function that is true of members of the set and false of other individuals. The alternative to an intensional set is an extensional set, which is defined by listing its elements.

For example, the class $chair$ is the set of all things that would be chairs. We do not want the definition to be the set of things that are chairs, because chairs that have not yet been built also fall into the class of chairs. We do not want two classes to be equivalent just because they have the same members. For example, the class of green unicorns and the class of chairs that are exactly 124 meters high are different classes, even though they may contain the same elements; they are both empty. A 124 meter high chair would not be a green unicorn.

The definition of class allows any set that can be described to be a class. For example, the set consisting of the number 17, the Tower of London, and the Prime Minister of Canada’s left foot may be a class, but it is not very useful. A natural kind is a class such that describing individuals using the class is more succinct than describing individuals without the class. For example, “mammal” is a natural kind, because describing the common attributes of mammals makes a knowledge base that uses “mammal” more succinct than one that does not use “mammal” and instead repeats the attributes for every individual.

Class $S$ is a subclass of class $C$ means that $S$ is a subset of $C$. That is, every individual of type $S$ is of type $C$.

The relationship between types and subclasses can be written as a definite clause:

You can treat $type$ and $subClassOf$ as special properties that allow property inheritance. Property inheritance occurs when a value for a property is specified at the class level and inherited by the members of the class. If all members of class $c$ have value $v$ for property $p$, this can be written in Datalog as

which, together with the aforementioned rule that relates types and subclasses, can be used for property inheritance.

Some general guidelines are useful for deciding what should be primitive and what should be derived:

• •

  When associating an attribute with an individual, select the most general class $C$ that the individual is in, where all members of $C$ have that attribute, and associate the attribute with class $C$. Inheritance can be used to derive the attribute for the individual and all other members of class $C$. This representation methodology tends to make knowledge bases more concise, and it means that it is easier to incorporate new individuals because members of $C$ automatically inherit the attribute.

• •

  Do not associate a contingent attribute of a class with the class. A contingent attribute is one whose value changes when circumstances change. For example, it may be true of the current computer environment that all of the computers come in cardboard boxes. However, it may not be a good idea to put that as an attribute of the $computer$ class, because it would not be expected to be true as other computers are bought.

• •

  Axiomatize in the causal direction. If a choice exists between making the cause primitive or the effect primitive, make the cause primitive. The information is then more likely to be stable when the domain changes. See Example 5.36.