Intelligent Problem Solvers in Education: Design Method and Applications - Intelligent Systems - page 127

properties or events of objects, and Rules is a set of deductive rules on facts. For example,
knowledge about a triangle consists of elements (angles, edges, etc) together with
formulas and some properties on them can be modeled as a class of C-objects whose sets
are as follows:

Attrs = {A, B, C, a, b, c, R, S, p, ...} is the set of all attributes of a triangle,

F = {A+B+C = ; a/sin(A) = 2R; b/sin(B) = 2R; c/sin(C) = 2R; a/sin(A) = b/sin(B); ... },

Facts = {a+b>c; a+c>b; b+c>a ; …},

Rules = { {a>b}  {A>B}; {b>c}  {B>C}; {c>a}  {C>A}; {a=b}  {A=B};
{a^2= b^2+c^2}  {A=pi/2}; {A=pi/2}  {a^2 = b^2+c^2, b  c}; ...}.

An object also has basic behaviors for solving problems on its attributes. Objects are
equipped abilities to solve problems such as:

1. Determines the closure of a set of attributes.

2. Executes deduction and gives answers for questions about problems of the form:

determine some attributes from some other attributes.

3. Executes computations

4. Suggests completing the hypothesis if needed.

For example , when a triangle object is requested to give a solution for problem {a, B, C}  S,
it will give a solution consists of three following steps:

Step 1: determine A, by A =  -B-C;
Step 2: determine b, by b = a.sin(B)/sin(A);
Step 3: determine S, by S = a.b.sin(C)/2;

3.1.2 Components of COKB model
Definition 3.2: The model for knowledge bases of computational objects (COKB model)
consists of six components:

(C, H, R, Ops, Funcs, Rules)

The meanings of the components are as follows:

 C is a set of concepts of computational objects. Each concept in C is a class of Com-

objects.

 H is a set of hierarchy relation on the concepts.

 R is a set of relations on the concepts.

 Ops is a set of operators.

 Funcs is a set of functions.

 Rules is a set of rules.

There are relations represent specializations between concepts in the set C ; H represents
these special relations on C . This relation is an ordered relation on the set C , and H can be
considered as the Hasse diagram for that relation.