Information Technology Reference
In-Depth Information
R
is a set of other relations on
C
, and in case a relation r is a binary relation it may have
properties such as reflexivity, symmetry, etc. In plane geometry and analytic geometry,
there are many such relations: relation “belongs to” of a point and a line, relation “central
point” of a point and a line segment, relation “parallel” between two line segments, relation
“perpendicular” between two line segments, the equality relation between triangles, etc.
The set
Ops
consists of operators on
C
. This component represents a part of knowledge
about operations on the objects. Almost knowledge domains have a component consisting
of operators. In analytic geometry there are vector operators such as addition, multiplication
of a vector by a scalar, cross product, vector product; in linear algebra there are operations
on matrices. The COKB model helps to organize this kind of knowledge in knowledge
domains as a component in the knowledge base of intelligent systems.
The set
Funcs
consists of functions on Com-objects. Knowledge about functions is also a
popular kind of knowledge in almost knowledge domains in practice, especially fields of
natural sciences such as fields of mathematics, fields of physics. In analytic geometry we
have the functions: distance between two points, distance from a point to a line or a plane,
projection of a point or a line onto a plane, etc. The determinant of a square matrix is also a
function on square matrices in linear algebra.
The set
Rules
represents for deductive rules. The set of rules is certain part of knowledge
bases. The rules represent for statements, theorems, principles, formulas, and so forth.
Almost rules can be written as the form “if <facts> then <facts>”. In the structure of a
deductive rule, <facts> is a set of facts with certain classification. Therefore, we use
deductive rules in the COKB model. Facts must be classified so that the component
Rules
can be specified and processed in the inference engine of knowledge base system or
intelligent systems.
3.1.3 Facts in COKB model
In the COKB model there are 11 kinds of facts accepted. These kinds of facts have been
proposed from the researching on real requirements and problems in different domains of
knowledge. The kinds of facts are as follows:
Fact of kind 1
: information about object kind. Some examples are ABC is a right
triangle, ABCD is a parallelogram, matrix A is a square matrix.
Fact of kind 2
: a determination of an object or an attribute of an object. The following
problem in analytic geometry gives some examples for facts of kind 2.
Problem: Given the points E and F, and the line (d). Suppose E, F, and (d) are determined.
(P) is the plane satisfying the relations: E (P), F (P), and (d) // (P). Find the general
equation of (P).
In this problem we have three facts of kind 3: (1) point E is determined or we have already
known the coordinates of E, (2) point F is determined, (3) line (d) is determined or we have
already known the equation of (d).
Fact of kind 3
: a determination of an object or an attribute of an object by a value or a
constant expression. These are some examples in plane geometry and in analytic
