Towards Qualitative Approaches to Bayesian Evidential Reasoning

A crucial aspect of evidential reasoning in crime investigation involves comparing the support that evidence provides for alternative hypotheses. Recent work in forensic statistics has shown how Bayesian Networks (BNs) can be employed for this purpose. However, the specification of BNs requires conditional probability tables describing the uncertain processes under evaluation. When these processes are poorly understood, it is necessary to rely on subjective probabilities provided by experts. Accurate probabilities of this type are normally hard to acquire from experts. Recent work in qualitative reasoning has developed methods to perform probabilistic reasoning using coarser representations. However, the latter types of approaches are too imprecise to compare the likelihood of alternative hypotheses. This paper examines this shortcoming of the qualitative approaches when applied to the aforementioned problem, and identifies and integrates techniques to refine them.

On Qualitative Probabilities for Legal Reasoning about Evidence

A crucial aspect of evidential reasoning in crime investigation involves comparing the support that evidence provides for alternative hypotheses. Recent work in forensic statistics has shown how Bayesian Networks (BNs) can be employed for this purpose. However, the specification of BNs requires conditional probability tables describing the uncertain processes under evaluation. When these processes are poorly understood, it is necessary to rely on subjective probabilities provided by experts. Accurate probabilities of this type are normally hard to acquire from experts. Recent work in qualitative reasoning has developed methods to perform probabilistic reasoning using coarser representations. However, the latter types of approaches are too imprecise to compare the likelihood of alternative hypotheses. This paper examines this shortcoming of the qualitative approaches when applied to the aforementioned problem, and identifies and integrates techniques to refine them.

Mechanising first-order temporal resolution

First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments. Although a complete and correct resolution-style calculus has already been suggested for this specific fragment, this calculus involves constructions too complex to be of practical value. In this paper, we develop a machine-oriented clausal resolution method which features radically simplified proof search. We first define a normal form for monodic formulae and then introduce a novel resolution calculus that can be applied to formulae in this normal form. By careful encoding, parts of the calculus can be implemented using classical first-order resolution and can, thus, be efficiently implemented. We prove correctness and completeness results for the calculus and illustrate it on a comprehensive example. An implementation of the method is briefly discussed.