A theoretical result [10] that relates tautological consequence in many-valued logics to the ideal membership problem in algebra is revisited. The intended use of the approach in this article and its implementation is the verification of consistency and the automated extraction of knowledge in rule-based knowledge systems. Programs are written in the CoCoA language. Four RBS are studied to illustrate the implementation.

Abstract.A package for investigating problems about configuration theorems in 3D-geometry and performing mechanical theorem proving and discovery is presented. It includes the preparation of the problem, consisting of three processes: defining the geometric objects in the configuration; determining the hypothesis conditions through a point-on-object declaration method; and fixing the thesis conditions. After this preparation, methods based both on Groebner Bases and Wu's method can be applied to prove thesis conditions or to complete hypothesis conditions. Homogeneous coordinates are used in order to treat projective problems (although affine and Euclidean problems can also be treated). A Maple implementation of the method has been developed. It has been used to extend to 3D some classic 2D theorems.

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