Belief Revision - Model-based Revision and Update

Model-based Revision and Update

A number of proposals for revision and update based on the set of models of the involved formulae were developed independently of the AGM framework. The principle behind this approach is that a knowledge base is equivalent to a set of possible worlds, that is, to a set of scenarios that are considered possible according to that knowledge base. Revision can therefore be performed on the sets of possible worlds rather than on the corresponding knowledge bases.

The revision and update operators based on models are usually identified by the name of their authors: Winslett, Forbus, Satoh, Dalal, Hegner, and Weber. According to the first four of these proposal, the result of revising/updating a formula by another formula is characterized by the set of models of that are the closest to the models of . Different notions of closeness can be defined, leading to the difference among these proposals.

Dalal

the models of having a minimal Hamming distance to models of are selected to be the models that result from the change;

Satoh

similar to Dalal, but distance between two models is defined as the set of literals that are given different values by them; similarity between models is defined as set containment of these differences;

Winslett

for each model of, the closest models of are selected; comparison is done using set containment of the difference;

Borgida

equal to Winslett's if and are inconsistent; otherwise, the result of revision is ;

Forbus

similar to Winslett, but the Hamming distance is used.

The revision operator defined by Hegner makes not to affect the value of the variables that are mentioned in . What results from this operation is a formula that is consistent with, and can therefore be conjoined with it. The revision operator by Weber is similar, but the literals that are removed from are not all literals of, but only the literals that are evaluated differently by a pair of closest models of and according to the Satoh measure of closeness.