A computer algebra approach to verification and deduction in many-valued knowledge systems

Abstract

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.

A Computer Approach to Mathematics Curriculum Developments Debugging

“…Therefore the system has discovered a detail that we, that considered that mastered the subject, had not taken into account! The situation is similar to rule based expert systems verification (Laita & Ledesma, 1997;Laita & Roanes-Lozano, 1999): an error in the knowledge of the expert cannot be detected at the verification step, but logical contradictions can be detected.…”

A Symbolic-Numeric Approach to MPL Continuous Logic and to Rule Based Expert Systems whose Underlying Logic is MPL

“…The logical and mathematical ideas behind the GB-based IE can be found in the mathematical model of logic and RBES in [2,3], that are based on previous works for rewriting classical Boolean [4,5] and many-valued logics [6].…”

“…Let us observe that we are going to consider the most general case, where: [2] x [1]_or_x [2] Note that in our previous works based on the theory for many-valued modal logics in [2,3], we have always considered that the rules and IC, as well as the given facts are stated as "true" (never as undertermined/undecided), although the forward reasoning is performed according to the many-valued modal logic chosen (modal connectives can appear within the antecedents and the consequents of the rules).…”

“…If the truth values of x [1] and x [3] The ¼ and ¾ would be the expected answers if we were thinking of probabilities and x [1] and x [2] were independent events.…”

“…For instance, we can check that ∨ is associative (observe that this is not formally a proof: we only check it for propositional variables x [1], x [2] and x [3]; nevertheless it will also hold if x [1], x [2] and x [3] are substituted by any polynomial expressions, so it will be true in general) 9 :…”