Editing Belief revision (section)

==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: [[Marianne Winslett|Winslett]], Forbus, Satoh, [[Mukesh Dalal|Dalal]], Hegner, and Weber. According to the  first four of these proposal, the result of revising/updating a formula <math>K</math> by another formula <math>P</math> is characterized by the set of models of <math>P</math> that are the closest to the models of <math>K</math>. Different notions of closeness can be defined, leading to the difference among these proposals.

; Peppas and [[Mary-Anne Williams|Williams]] : provided the formal relationship between revision and update. They introduced the Winslett Identity in the [[Notre Dame Journal of Formal Logic]].<ref name=":0">{{cite journal |doi=10.1305/ndjfl/1040308831 |mr=1359110 |zbl=0844.03017|title=Constructive Modelings for Theory Change |journal=Notre Dame Journal of Formal Logic |volume=36 |pages=120–133 |year=1995 |last1=Peppas |first1=Pavlos |last2=Williams |first2=Mary-Anne |doi-access=free }}</ref>

; Dalal : the models of <math>P</math> having a minimal [[Hamming distance]] to models of <math>K</math> 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 <math>K</math>, the closest models of <math>P</math> are selected; comparison is done using set containment of the difference;

; Borgida : equal to Winslett's if <math>K</math> and <math>P</math> are inconsistent; otherwise, the result of revision is <math>K \wedge P</math>;

; [[Ken Forbus|Forbus]] : similar to Winslett, but the Hamming distance is used.

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