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.