| This paper is concerned with expounding a new
representation paradigm for modelling expert systems based on computing
Groebner Bases. Previous research on Groebner Bases expert systems has
so far been connected to modelling expert systems based on (both bi- and
multi-valued) propositional logics. Our approach instead is based on
the well-known Artificial Intelligence frames paradigm for representing
knowledge. More precisely, our research is based on translating an
already existent expert system described in terms of the frames 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 frames-based paradigm than it was in previous
propositional logic-based expert systems.
The exposition is illustrated with some interesting examples in which
the main advantages of our model are established by comparing its
performance to that of the mentioned propositional logic-based expert
systems.
Acknowledgments
This work was partially supported by the research project UCM2008-910563 (UCM - BSCH Gr. 58/08, research group ACEIA). |