Belief Base Change on Implicant Sets: How to Give Up Elements of a Belief Based on Literal Level

We present a formal framework for belief revision in terms of sets of implicants, where an implicant is a finte set of literals. We define binary revision functions on implicant sets and we formulate implicant revision postulates that specify properties every revision function should have. We reformulate the revision postulates introduced by Alchurron, Gardenfors and Makinson (AGM revision postulates, [2]) a in terms of operations on model sets and we define revision postulates for implicant sets that characterize AGM revision operations. Then we consider distance based revision functions and in particular those based on the symmetrical difference between interpretations. We show that the minimal symmetric difference between the model sets of two implicants can be obtained by a simple binary operation on these implicants. The representation of a formula by implicants is not unique (our approach does not relay on prime implicants neither on the set of all prime implicants of a formula). We show that our implicant revision approach obtains the same revision result operated on different equivalent implicant sets.