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.

Reasoning about Requirements Evolution Using Clustered Belief Revision

During the development of system requirements, software system specifications are often inconsistent. Inconsistencies may arise for different reasons, for example, when multiple conflicting viewpoints are embodied in the specification, or when the specification itself is at a transient stage of evolution. These inconsistencies cannot always be resolved immediately. As a result, we argue that a formal framework for the analysis of evolving specifications should be able to tolerate inconsistency by allowing reasoning in the presence of inconsistency without trivialisation, and circumvent inconsistency by enabling impact analyses of potential changes to be carried out. This paper shows how clustered belief revision can help in this process. Clustered belief revision allows for the grouping of requirements with similar functionality into clusters and the assignment of priorities between them. By analysing the result of a cluster, an engineer can either choose to rectify problems in the specification or to postpone the changes until more information becomes available.

Herbrand's Theorem and Equational Reasoning: Problems and Solutions

The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the so-called simultaneous rigid E-unification problem. In the second part, we survey recent result on the simultaneous rigid E-unification problem.