On the implementation of the belief change operators

Abstract

In this article we will introduce certain considerations that must be taken into account while implementing the change operations of the belief change theory. The abstract models of bellief change make no considerations in respecto to the internal structures of the beliefs that compound the knowledge of an agent, and much less take into account the computational complexity of the proposed algorithms. In this article we will explicitly introduce some of the inconveniences and the possible solutions that can be found while implementing the change operations. Firstly, we will introduce the different change operations of the AGM model. These operations are characterized by certain rationality postulates that determine their behavior on the knowledge level. This means that the change operations are specified entirely in terms of the knowledge content (beliefs), making no distinction between the explicit imformation and the implicit information. In second term, we will introduce the change operations applicable to knowledge bases (that is, finite sets not necessarily closed under logical cnsequence) in which the explicit beliefs of the konwledge base are clearly distinguished from the beliefs deduced from them. In this case the change operations are defined on a symbolic level, which contains, explicit references about the syntax of the sentences that compound the base. We will see how certain postulates defined on the knowledge level must be transfomed into less restrictive postulates with the objective of respecting the basic principles of the AGM model: minimun change, syntax irrelevancy and adequacity of konwledge representation. We will also introdece a meta-symbolic level where we preach about the behavior of the sentenes that compund a knowledge base, making no reference to its syntactic form. Lastly, we will analyze the change operations on the implementation level. On this level, it is necessary to make certain decision that are not considered not only on the knowledge level but also on the symbolic level. This analysis is of vital importance because the decisions that are made on the implementation level can have a strong impact on the knowledge level.