Interpretation

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## Interpretation

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 .

Second, must ``satisfy'' the conditions and axioms given in this chapter and the remaining chapters of this document. As a start, this includes the following conditions.

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).

Vishal I. Sikka
Wed Dec 7 13:23:42 PST 1994