TITLE: An algebraic approach for detecting potential dangerous situations in
expert systems through Groebner bases.

AUTHOR: Antonio Hernando, Roberto Maestre-Martínez, Eugenio Roanes-Lozano

EXTENDED ABSTRACT:
The aim of this work is to present theoretically a new algebraic method
for detecting potentially 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. Our work is based on a previous result obtained for detecting
possible inputs which involve dangerous situation. In this way the work
presented here can be considered as an extension of this previous result.

The method presented here is based on calculating just one reduced
Groebner basis of a polynomial ideal representing the system's
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
potentially 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. An example of implementation in the computer algebra
system CoCoA is included.