Adams Conditioning and Likelihood Ratio Transfer Mediated Inference
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Forensic science advocates the use of inference mechanisms which may be viewed as simple multi-agent protocols. An important protocol of this kind involves an agent FE (forensic expert) who communicates to a second agent TOF (trier of fact) first its value of a certain likelihood ratio with respect to its own belief state which is supposed to be captured by a probability function on FE's proposition space. Subsequently FE communicates its recently acquired confirmation that a certain evidence proposition is true. The inference part of this sort of reasoning, here referred to as likelihood ratio transfer mediated reasoning, involves TOF's revision of its own belief state, and in particular an evaluation of the resulting belief in the hypothesis proposition. Different realizations of likelihood ratio transfer mediated reasoning are distinguished: if the evidence hypothesis is included in the prior proposition space of TOF then a comparison is made between understanding the TOF side of a belief revision step as a composition of two successive steps of single likelihood Adams conditioning followed by a Bayes conditioning step, and as a single step of double likelihood Adams conditioning followed by Bayes conditioning; if, however the evidence hypothesis is initially outside the proposition space of TOF an application of proposition kinetics for the introduction of the evidence proposition precedes Bayesian conditioning, which is followed by Jeffrey conditioning on the hypothesis proposition.
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