  A detailed exposition of foundations of a logic-algebraic model for reasoning
with knowledge bases specified by propositional (Boolean) logic is presented.
The model is conceived from the logical translation of usual derivatives on
polynomials (on residue rings) which is used to design a new inference rule of
algebro-geometric inspiration. Soundness and (refutational) completeness of the
rule are proved. Some applications of the tools introduced in the paper are
shown.
