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The aim of this work is to present theoretically a new algebraic method for detecting nearly dangerous states in an expert system whose knowledge is represented by propositional Boolean logic. Given a dangerous state which does not happen at present, our method is able to detect if a dangerous situation would happen if an input variable of the Expert System changed. The method presented here is based on calculating just one Groebner basis of a polynomial ideal representing the system knowledge. In this way, although the Expert System is designed to notify only dangerous situations, we have developed an algebraic model for including in the expert system the ability to recommend watching carefully some Boolean variables such that if one of them changed, the system would fall in a dangerous situation. In this way, the same expert system not only warns about dangerous situations but also about nearly dangerous situations. It may be noted that our method does not require to change the Expert System for including this facility. As far as our knowledge goes, our work is completely new in the field of Expert Systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with expounding a new representation paradigm for modeling expert systems based on computing Groebner Bases. Previous research on Groebner Bases expert systems has so far been connected to modeling expert systems based on propositional logics. Our approach instead is based on the well-known Artificial Intelligence ‘Concept-Attribute-Value’ paradigm for representing knowledge. More precisely, our research is based on translating an already existent expert system described in terms of the ‘Concept-Attribute-Value’ paradigm to a new algebraic model which represents knowledge by means of polynomials. In this way, issues about consistence and inference within this expert system will be, through this new model, transformed into algebraic problems involving calculating Groebner Bases. By using this new model of ours, some interesting advantages ensue: on the one hand, knowledge representation may be performed in a more straightforward and intuitive way; on the other, calculating the Groebner Bases associated to our algebraic model is usually faster adopting this new ‘Concept-Attribute-Value’-based paradigm than it was in previous propositional logic-based expert systems. [Copyright &y& Elsevier]