Prime forms and minimal change in propositional belief bases

This paper proposes to use prime implicants and prime implicates normal forms to represent belief sets. This representation is used, on the one hand, to define syntactical versions of belief change operators that also satisfy the rationality postulates but present better complexity properties than those proposed in the literature and, on the other hand, to propose a new minimal distance that adopts as a minimal belief unit a “fact”, defined as a prime implicate of the belief set, instead of the usually adopted Hamming distance, i.e., the number of propositional symbols on which the models differ. Some experiments are also presented that show that this new minimal distance allows to define belief change operators that usually preserve more information of the original belief set.