An algebraic model for implementing expert systems based on the knowledge of different experts

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 Groebner bases on an ideal of polynomials.