A Method of Logic Deduction and Verification in KBS Using Positive Integers

Abstract

Classic propositional Boolean algebra is modelized in this paper as a subset of IN (the divisors of a certain product of prime numbers) with operations gcd and lcm. The isomorphism is constructed in a way that recalls Godel numbers. This approach can be used to study logic deduction and to check the consistency of Rule-Based Knowledge Based Systems. An implementation in the Computer Algebra system Maple, that uses intensively exact arithmetic, is included as an appendix. Although the growth of the integers involved makes this implementation interesting only if the number of propositional variables is not greater than 8, we think its simplicity makes it very interesting to illustrate KBS behaviour.