An Algebraic Model for implementing Expert Systems based on the Knowledge of
different Experts.
Antonio Hernando, Eugenio Roanes-Lozano
Keywords: Expert Systems, Groebner Basis, Boolean logic
The aim of this paper is to expound an original algebraic model for managing
the knowledge provided by different expert humans when developing expert
systems. This model is conceived as an extension of classical propositional
logics in which each proposition is associated with a set of human experts who
agree with it. In our model, the logical notions of tautological consequence
and consistency of a set of formulae are reformulated taking into account
the criteria and the knowledge of the different experts. The core of the
paper is related to the discovery of a remarkable relation between these
redefined logical concepts with the calculation of reduced Groebner bases
on an ideal of polynomials.
Expert systems are computational programs on a certain domain which try to
simulate the decisions that human experts on this domain would take. In the
last years, much research has been focused on developing both techniques
for representing the human knowledge in a computer and techniques for
reasoning automatically.
An interesting way for representing knowledge in an expert system is based on
describing it through propositional logic. By means of a mathematical result,
an expert system based on > propositional logic can be transformed to an
algebraic problem. In this way, expert systems based on propositional logic
may be very easy implemented by means of a computer algebra system like CoCoA
or Polybori. Making use of this result, different expert systems have been so
far developed in the last recent years.
In some interesting domains very related to the development of experts
systems, like medicine, different human experts may have different criteria
or opinions in some points which may lead to different conclusions or
which may be even contradictory. In order to manage the different criteria
of these experts, we have extended the propositional logic redefining the
concepts of consistence and tautological consequence. Taking into account
this logical concepts, we have obtained a relation to the calculation of
Groebner basis. This results allows us to deal algebraically the development
of this expert systems which takes into account the criteria of different
human experts.