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.

Revision rules in the theory of evidence

Combination rules proposed so far in the Dempster-Shafer theory of evidence, especially Dempster rule, 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 a 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. Although belief revision is already an important subfield of artificial intelligence, so far, it has been little addressed in evidence theory. In this paper, we define the notion of revision for the theory of evidence and propose several different revision rules, called the inner and outer
revisions, and a modified adaptive outer revision, which better corresponds to the idea of revision. Properties of these revision rules are also investigated.

Dazed and Confused: Accidental Mixtures of Goods and the Theory of Acquisition of Title

This paper explores the law of accidental mixtures of goods. It traces the development of the English rules on mixture from the seminal nineteenth century case of Spence v Union Marine Insurance Co to the present day, and compares their responses to those given by the Roman law, which always has been claimed as an influence on our jurisprudence in this area. It is argued that the different answers given by English and Roman law to essentially the same problems of title result from the differing bases of these legal systems. Roman a priori theory is contrasted with the more practical reasoning of the common law, and while both sets of rules are judged to be coherent on their own terms, it is suggested that the difference between them is reflective of a more general philosophical disagreement about the proper functioning of a legal system, and the relative importance of theoretical and pragmatic considerations.

Explaining binge drinking among adolescent males using the Theory of Planned Behaviour

Binge drinking among adolescents in Northern Ireland is prevalent and has detrimental eff ects on public health. Health education interventions, based on valid explanatory models of health behaviour, are required to reduce binge drinking behaviour among adolescents. " is paper examines the utility of the " eory of Planned Behaviour in explaining binge drinking behaviour among adolescent males. Using questionnaire responses from 94 adolescent boys attending secondary schools in the Belfast area, logistic regression modelling suggested that the " eory of Planned Behaviour explained 36% of the variance in self-reported binge drinking behaviour. Attitudes towards binge drinking were the strongest predictor of binge drinking behaviour. Tackling attitudes about binge drinking is a challenge to be considered when designing interventions to reduce binge drinking among this population