K = (A, P, T), where A = {Course, AdvCourse, BasCourse, Professor, Student, GradStudent, Undergrad, String},
P = {enrolls, taughtby, degree},
and the set T of assertions consists of:
Course
∀taughtby.(Professor ∪ Grad Student) ∩ ∃= ¹ taughtby AdvCourse  ≥  Course Π Venrolls.(GradStudent Π ¬Undergrad) Π ∃≤ 20 enrolls BasCourse     Course Π Vtaughtby.Professor GradStudent

![0_image_0.png](0_image_0.png)

Undergrad Y Student Figure 3:  The ALUNI knowledge base corresponding to the KEE knowledge base in Figure 2 is mapped into the class expression 0(F 1 ) Π · · · Π 0 (F k ) Π
∀θ( S 1 ).θ( H 1 ) ∩ ∃≥ m :θ( S 1 ) ∩ ∃≤ π :θ( S 1 )  Π

$\mathcal{L}_{\text{max}}$
∀θ( S k ) θ( H k ) Π ∃≥π k θ( S k ) Π ∃≤π k θ( S k ).

This mapping allows us to translate a frame knowledge base into an ALUNI knowledge base, as specified in the following definition.

Definition 3.4 The ALUNI knowledge base θ( F ) = ( A, P, T ) corresponding to a frame knowledge base F is obtained as follows:
A consists of one atomic concept θ( F ) for each frame name F in F .

- P consists of one atomic role θ( S ) for each slot name S in F .

- T consists of an inclusion assertion
0(F)
for each frame definition Frame :  F in KB F
E
in F.

Example 3.2 (cont.) We illustrate the translation on the frame knowledge base in Figure 2. The corresponding ALUNI knowledge base is shown in Figure 3.

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