Imprecise probabilistic query answering using measures of ignorance and degree of satisfaction

In conditional probabilistic logic programming, given a query, the two most common forms for answering the query are either a probability interval or a precise probability obtained by using the maximum entropy principle. The former can be noninformative (e.g.,interval [0; 1]) and the reliability of the latter is questionable when the priori knowledge isimprecise. To address this problem, in this paper, we propose some methods to quantitativelymeasure if a probability interval or a single probability is sufficient for answering a query. We first propose an approach to measuring the ignorance of a probabilistic logic program with respect to a query. The measure of ignorance (w.r.t. a query) reflects howreliable a precise probability for the query can be and a high value of ignorance suggests that a single probability is not suitable for the query. We then propose a method to measure the probability that the exact probability of a query falls in a given interval, e.g., a second order probability. We call it the degree of satisfaction. If the degree of satisfaction is highenough w.r.t. the query, then the given interval can be accepted as the answer to the query. We also prove our measures satisfy many properties and we use a case study to demonstrate the significance of the measures. © Springer Science+Business Media B.V. 2012

A-level Mathematics Module Choice and Subsequent Performance in First Year of an Engineering Degree

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules. The flexibility in choice of applied modules has led to concerns that many students would proceed to study engineering at university with little background in mechanics. A survey of aerospace and mechanical engineering students in our university revealed that a combination of mechanics and statistics (the basic module in both) was by far the most popular choice of optional modules in A-level Mathematics, meaning that only about one-quarter of the class had studied mechanics beyond the basic module within school mathematics. Investigation of student performance in two core, first-year engineering courses, which build on a mechanics foundation, indicated that any benefits for students who studied the extra mechanics at school were small. These results give concern about the depth of understanding in mechanics gained during A-level Mathematics.

European Labour Law, 3rd edition

This textbook on European Labour law adds to the existing literature in two aspects. First, it is written in such a way that readers who are versed in EU law and labour law, as well as those who only know national labour law can profit. Secondly, it analyses the EU's contribution to labour law from comparative and EU integration perspectives, taking a critical approach to the EU's so-called economic constitution as shaped by its Court of Justice.