An *interpretation* is a function that associates the
constants of KIF with the elements of a conceptualization. In order
to be an interpretation, a function must satisfy the following two
properties.

First, the function must map constants into concepts of the appropriate type. It must map object constants into objects in the universe of discourse. It must map function constants into functions on the universe of discourse. It must map relation constants into relations on the universe of discourse. Notice that we allow for functions and relations of variable, finite arity. The function must map logical constants into one of the boolean values or (which may or may not be members of the universe of discourse).

- 1. If is an object constant, then .
- 2. If is a function constant, then
.
- 3. If is a relation constant, then .
- 4. If is a logical constant, then .

Every interpretation must map every numerical constant into the corresponding number (assuming base 10).

Every interpretation must map the object constant `bottom` into

.

Every interpretation must map the logical constant `true` into

and the logical constant `false` into

.

Note that, even with these restrictions, KIF is only a ``partially interpreted'' language. Although the interpretations of some constants (the basic constants) are constrained in the definition of the language, the meanings of other constants (the non-basic constants) are left open (i.e. left to the imaginations of the language users).

Wed Dec 7 13:23:42 PST 1994