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(2008), Michel Chein & Marie-Laure Mugnier (2009) and Frank van Harmelem & Vladimir &
Bruce (2008) we have found popular methods for knowledge representation. They include
predicate logic, semantic nets, frames, deductive rules, conceptual graphs. The above
methods are very useful for designing intelligent systems, especially intelligent problem
solvers. However, they are not suitable to represent knowledge in the domains of reality
applications in many cases, especially the systems that can solve problems in practice based
on knowledge bases. There have been new models proposed such as computational
networks, networks of computational objects in Nhon Van Do (2009) and model for
knowledge bases of computational objects (COKB) in Nhon Van Do (2010).
The COKB model can be used to represent the total knowledge and to design the knowledge
base component of practical intelligent systems. Networks of computational objects can be
used for modeling problems in knowledge domains. These models are tools for designing
inference engine of systems. The models have been used in designing some intelligent
problem solvers in education (IPSE) such as the program for studying and solving problems
in Plane Geometry in Nhon (2000), the program for solving problems about alternating
current in physics. These applications are very easy to use for students in studying
knowledge, to solve automatically problems and give human readable solutions agree with
those written by teachers and students. In this section, the COKB model and computational
networks, that are used for designing IPSE will be presented in details.
3.1 COKB model
The model for knowledge bases of computational objects (COKB) has been established from
Object-Oriented approach to represent knowledge together with programming techniques
for symbolic computation. There have been many results and tools for Object-Oriented
methods, and some principles as well as techniques were presented in Mike (2005). This
way also gives us a method to model problems and to design algorithms. The models are
very useful for constructing components and the whole knowledge base of intelligent
system in practice of knowledge domains.
3.1.1 Computational objects
In many problems we usually meet many different kinds of objects. Each object has
attributes and internal relations between them. They also have basic behaviors for solving
problems on its attributes.
Definition 3.1: A computational object (or Com-object) has the following characteristics:
1.
It has valued attributes. The set consists of all attributes of the object O will be denoted
by M(O) .
2.
There are internal computational relations between attributes of a Com-object O. These
are manifested in the following features of the object:
-
Given a subset A of M(O). The object O can show us the attributes that can be
determined from A.
-
The object O will give the value of an attribute.
-
It can also show the internal process of determining the attributes.
The structure computational objects can be modeled by ( Attrs, F, Facts, Rules ). Attrs is a set
of attributes, F is a set of equations called computation relations, Facts is a set of
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