Accumulation and inference over finite-generated algebras for mapping approximations

Abstract

In this paper we propose a generalization of Belnap's method in which we assign values to the elements of a Boolean Algebra of Propositions to represent the partial knowledge known of a valuation over the algebra. This generalizations includes mappings that are not a homomorphism respect to all the operations, but only respect to some, like the measures of possibility or of necessity. We also propose the generalization of the method by which we can refer to and accumulate all the available information of a set of generators. This will let us make inferences of valid approximations.