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The coefficient of x has a set of roots:
{2 , 2}
+ if parameter m2
  , then:
“This equation has no root”
+ if parameter m , then:
“This equation has set of roots is the set of real numbers ”
+ if parameter
m2 , 2

, then:

2m
1
x
2
m2
m4
6. Conclusions and future work
In this chapter, we proposed a method for designing intelligent problem solvers (IPS),
especially those in education (IPSE). These systems have suitable knowledge base used by
the inference engine to solve problems in certain knowledge domain, they not only give
human readable solutions of problems but also present solutions as the way instructors and
learners usually write them. Knowledge bases contain concepts of computational objects
(Com-Objects), relations, operators, functions, facts and rules. The Computational Object
Knowledge Base model (COKB) and its specification language can be used for knowledge
modeling, for designing and implementing knowledge bases. The COKB model has been
established from Object-Oriented approach for knowledge representation together with
programming techniques for symbolic computation. The design of inference engine requires
to model problems and to design reasoning algorithms with heuristics and sample
problems. Computational networks (Com-Net) and networks of computational objects (CO-
Net) can be used effectively for modeling problems and construction of reasoning
algorithms in practical knowledge domains. These models are tools for designing inference
engine of systems.
The proposed design method has been used to produce applycations in many fields such as
mathematics, physics and chemistry. They support studying knowledge and solving
problems automatically based on knowledge bases. Users only declare hypothesis and goal
of problems base on a simple language but strong enough for specifying problems. The
programs produce a human readable solution, which is easy to read and agree with the way
of thinking and writing by students and instructors.
Designing an intelligent problem solver in education is a very challenging task, as domain
knowledge and human thinking are very complicated and abstract. There are domains of
knowledge with functional attributes such as knowledge of alternating current in physics.
This motivates another extensions of COKB model, Com-Net and CO-Net, and develops
design techniques. They will accept simple valued variables and also functional variables.
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