Abstract
In this paper, the well-known Radical Membership Problem of Commutative Algebra is adapted to develop an implementation of the inference processes in Knowledge Based Systems.
Let ∑ be a set of propositions, Γ a proposition, and let us denote their images, in a certain isomorphism, by σ and γ respectively. It can be established whether or not Γ follows from ∑ (∑ ⊢ Γ) by checking the equality of ideals <σ∪{1{it-t·γ}>=<1> in the polynomial model (t is a new variable). As a consequence, a criterion for consistency is obtained.
Work partially supported by DGICYT (Spain), project PB-94-0424.
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Roanes-Lozano, E., Laita, L.M., Roanes-Macías, E. (1996). An inference engine for propositional two-valued logic based on the radical membership problem. In: Calmet, J., Campbell, J.A., Pfalzgraf, J. (eds) Artificial Intelligence and Symbolic Mathematical Computation. AISMC 1996. Lecture Notes in Computer Science, vol 1138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61732-9_51
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DOI: https://doi.org/10.1007/3-540-61732-9_51
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