An algebraic method for managing reliability in propositional logics

Abstract

The aim of this paper is to expound an original algebraic model for managing information with different degrees of unreliability. This model is conceived as an extension of classical propositional logics in which each propositional formula is associated with an unreliability value, and results in an approach quite different from that of probabilistic logics. In our model, the logical notions of tautological consequence and consistency of a set of formulae are reformulated on behalf of the foreseen unreliability values. The core of the paper is related to the discovery of a remarkable relation between these unreliability values associated to tautological consequence and the calculation of the reduced Groebner basis of a polynomial ideal. In this way, our method for assigning these unreliability values to information and reasoning turns out to have a straightforward translation into algebraic terms.