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.

Fast ion acceleration from thin foils irradiated by ultra-high intensity, ultra-high contrast laser pulses

Ion acceleration resulting from the interaction of ultra-high intensity (2 x 10(20) W/cm(2)) and ultra-high contrast (similar to 10(10)) laser pulses with 0.05-10 mu m thick Al foils at normal (0 degrees) and 35 degrees laser incidence is investigated. When decreasing the target thickness from 10 mu m down to 0.05 mu m, the accelerated ions become less divergent and the ion flux increases, particularly at normal (0 degrees) laser incidence on the target. A laser energy conversion into protons of,similar to 6.5% is estimated at 35 degrees laser incidence. Experimental results are in reasonable agreement with theoretical estimates and can be a benchmark for further theoretical and computational work. (C) 2011 American Institute of Physics. [doi:10.1063/1.3643133]