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In a previous paper [LR1] we presented a theoretical model for propositional Boolean algebras, based on techniques from Commutative Algebra.
It was adapted to check the forward reasoning consistency of a given Knowledge Based System (KBS) based on bivalent logic [LR2]. Surprisingly, verification is usually hand made, for example ``visually", with the help of diagrams.
The paper below begins with a brief resume of those results. A brand new implementation based in Maple V is described afterwards. This description pays special attention to the algebraic details of the implementation. The procedures are given in full detail.
There is a great advantage with respect to working just with rewriting techniques, such as those used in Maple's ``Logic package". To approach the problem using ideals and class rings makes it possible to go further and directly modelize the algebra associated to a KBS as a polynomial Boolean algebra (that is also a k-algebra).

Andre Heck
Sun Apr 23 10:32:10 MDT 1995