Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence

Belief revision characterizes the process of revising an agent’s beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation
is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster
rule of combination, just like revision in the sense of Alchourron, Gardenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey’s rule of updating, Dempster rule of conditioning and a form of AGM revision.

Integração de evidências em redes credais e a regra de Jeffrey

Credal networks provide a scheme for dealing with imprecise probabilistic models. The inference algorithms often used in credal networks compute the interval of the posterior probability of an event of interest given evidence of the specific kind -- evidence that describe the current state of a set of variables. These algorithms do not perform evidential reasoning in case of the evidence must be processed according to the conditioning rule proposed by RC Jeffrey. This paper describes a procedure to integrate evidence with Jeffrey's rule when performing inferences with credal nets.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont. A. Jeffrey says that he will be able to supply Mr. Woodruff with glass and iron pipe, June 7, 1875.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont.

Letter to S.D. Woodruff from A. Jeffrey importer of Hardware, Iron, Steel, and Window Glass of St. Catharines, Ont. regarding breakage and freight, June 23, 1875.

Unsigned letter to A. Jeffrey written on an envelope stating that the glass was free from breakage, therefore there would be a deduction of 10 percent

Unsigned letter to A. Jeffrey written on an envelope stating that the glass was free from breakage, therefore there would be a deduction of 10 percent, June 28, 1875.

Receipt from A. Jeffrey importer of Hardware, Iron, Steel, Nails and etc

Receipt from A. Jeffrey importer of Hardware, Iron, Steel, Nails and etc. regarding payment received on glass panes, Nov. 12, 1875.

Receipt from A. Jeffrey of St. Catharines

Receipt from A. Jeffrey of St. Catharines regarding payment for screws and white glue, June 30, 1876.

Receipt from A. Jeffrey, Hardware, St. Catharines

Receipt from A. Jeffrey, Hardware, St. Catharines for hardware items, April 1, 1887.