The aim of Belief Merging is to aggregate possibly conflicting pieces of information issued from different sources. The quality of the resulting set is usually considered in terms of a closeness criterion between the resulting belief set and the initial belief sets. The notion of distance between belief sets is thus a crucial issue when we face the merging problem. The aim of this paper is twofold: introducing a syntactical way to calculate distances and proposing the use of a distance based on prime implicants and prime implicates that considers the importance of each propositional symbol in the belief set.

In this paper we present a syntactical way to develop the adaptation capability in logical-based intelligent agents. We use prime implicants to represent the beliefs of an agent and present how syntactical belief update operators can be obtained by correlating models and prime implicants. Using prime implicants allows the introdution a new notion of belief update. We characterize this new operator both in terms of postulates and in terms of explicit operators.